Architecturally, the back of the Westside Plaza shopping centre in Edinburgh's Wester Hailes owes a lot to Guantánamo Bay. Big, grey, squat blocks covered in pipes and ducting, no windows, no doors, nothing to reveal what it is. Hostile and bunkerish, it feels like a place of punishment. It's a drizzly Saturday in April and no one's about. On the road beyond, a bus goes past. "Try prayer," it says.

Inside, Westside still feels like a detention centre, but at least there are people around and the shops are open. On the steps by the front entrance, splayed against the concrete, stands a crowd, facing towards the Pentland Hills. They're mostly male, mostly white, mostly wearing blue anoraks or carrying little flags printed with the word yes. Scan the crowd and the word is repeated over and over: yes yes yes yes yes. Like a very polite orgasm.

One of the peculiarities of the coming Scottish referendum on independence is the effect it has had on language. The yes campaign is led by the Scottish National party under first minister Alex Salmond but also includes the Greens, the Scottish Socialist party and the Radical Independence Campaign. The no campaign includes everyone else. Its official name is Better Together, though it's known to its friends as Bitter Together. So there are yesses and there are noes, there are a lot of unsures and – decreasingly – there are a few not bothereds. Which means that, whatever happens when Scotland votes on 18 September, the country will already have found itself in wild new semantic landscapes: "So I'm a no, I know you're a no, but your wife's a yes and your kids are half yes, half no. Yes?" "Aye. Kind of. No."

Wester Hailes is the third of the yes campaign's Super Saturdays, big gatherings of local activists out to galvanise voters. It's an impressive turnout for a wet weekend morning six months before the vote, more than 100 people chatting under the windy gazebos. I follow MSP Gordon MacDonald (numberplate G2 SNP) out on to the streets. It's a mixed area, partly private houses, partly the two- or three-storey tenement council flats found all over Scotland. MacDonald canvasses like the old pro he is, knocking on doors, polite and friendly, a wee joke here, a knowing local reference there.

Of those who are awake and prepared to do more than stand behind the curtains pretending they haven't heard the doorbell, it's a mixed crop, some undecided, some deranged. "I'm too old to be bothered," says a healthy-looking woman in her 60s. "I'll be dead in five years, so what do I care?" One person complains about 16-year-olds getting the vote. An elderly man with a comb-over says he'd vote yes if someone could set his mind at ease over the currency question. Two women say they don't trust Alex Salmond. "Well," MacDonald says, "if we get independence, by 2016 we'll have our own government and you can vote in whoever you like." One man, busy wrangling kids and scooters, says he's a yes: "If we're going to fall flat on our faces, we might as well do it ourselves."

Most people are happy to debate the points and most are well-informed. One woman mentions the deficit; another is worried about Scotland getting into a second Darien Scheme, the disastrous 17th-century colonial venture that pushed Scotland to the edge of bankruptcy and into union with England. "Five yesses," crows another activist. No one here rants, no one shouts and, apart from a Scottish Defence League member who tells us we're all fucking scum, everything remains as cordial as an episode of Gardeners' Question Time.

James Reekie, Conservative, voting no. Photograph: Robert Ormerod for the Guardian

For a politician, this place might be the promised land. A whole country obsessed with politics. Not just taking a stand and thinking about the issues, but actually demanding more – more figures, more data, more information. Families split down the middle, couples making contingency plans, arguments in the supermarket over taxation.

In four months' time, the people of Scotland will decide whether they want their country to be independent. Yes/no. Nothing in between. There had once been the possibility of a third option, devo max (greater powers but not total detachment from Westminster), but after some lively horse trading it was settled. Yes or no, stay or go.

It looks as if such a stark choice is doing what it was supposed to: concentrate minds, get everyone going. All the signs are for a high turnout. Back at the end of last year, the polls were holding steady: a third of the country wanted independence, the rest wanted to remain within the UK. Now the gap is narrowing. Many of those who might refuse to vote in a general election see this as an apolitical issue, bigger than one party or one politician. The young are beginning to get involved, turning out to canvass or door-knock. The Indy Ref, as the Scottish papers call it, is doing what party politics never could and politicising a whole generation.

Whether it's a yes or a no vote, it's those young activists who will inherit the aftermath and define the shape Scotland takes. So what exactly do they want? Why is the question even being asked? And – since Britain is still a small island, no matter which way you slice it – how come things look so very different in London and in Lerwick?

Roisin McLaren is 19 and president of the Edinburgh University Scottish Nationalist Association. We meet in the Elephant House on the Mound, the cafe where adoptive Scot JK Rowling is supposed to have written much of the Harry Potter series and that has some of the oddest loo graffiti in Britain: "Of course it is happening inside your head, Harry. But why on Earth should that mean it is not real?"

McLaren is vivid and fierce, and comes prepared for battle. She's from a political family, her mother a Scottish socialist, her dad was in the Communist Party of Great Britain, a grandmother a lifelong SNP supporter, and family members campaigned in 1979 for the devolution referendum. She says one recalls "being laughed off the doorstep. Don't be daft! It was a left-of-centre, loony idea. And now it's a serious possibility."

Since New Labour's 1997 referendum on establishing a separate parliament, devolution has been introduced in stages. Which means that government in Scotland is in a state of perpetual movement, with a parliament at Holyrood and a party in power, but no constitution or control over issues such as energy and blowing things up. Westminster's initial hope was that devolution would kill nationalism. Instead, the opposite happened. The SNP's landslide victory in the 2011 Holyrood elections astounded even its leaders.

"When I started campaigning a year ago, I didn't think it was winnable," McLaren says. "People weren't interested. But that's changed. In the past, you could barely give people a leaflet. Now they're coming up to us and asking questions."

Anya O’Shea, Labour, voting no. Photograph: Robert Ormerod for the Guardian

She's also had help from unexpected quarters. David Cameron's speech at the Olympic velodrome in February, in which he urged the rest of Britain to tell their Scottish friends to keep the Union, was, she says, "such a bad move. I got people that were voting no coming up to me and saying it went down so badly." Why? "Because it was an English twat telling us all what to do. It was a toff Tory politician, who nobody here likes or voted for, saying, 'Oh, England, please tell Scotland to stay in the UK because we love you so much.' Fuck off!" Is there anything he could have said that would have made a difference? "No. If he'd had any sense, he would have kept his gob shut."

This view is echoed elsewhere. It seems it isn't so much that the yes camp is running a good campaign as that the no camp is running a bad one. Its latest strategy is to tell Scotland it's naughty for thinking of leaving the Union, and to remind it of its debts and debtors. That ploy is currently led by Alistair Darling, ex-Labour chancellor. Everyone agrees he is a safe pair of hands, and great with sums, but he's a charisma-free character leading a charisma-free campaign. Of all the people I spoke to, not one mentioned Darling. Instead, they talked about Salmond – and Cameron.

As McLaren points out, the Tories are seen as having no mandate in Scotland. The current joke is that there are more pandas here than Tory MPs. Election after election, the Scots return Labour, SNP and Lib Dem MPs – and get Westminster governments for which they feel they didn't vote.

Like the Darien Scheme, that old antipathy to the Tories is a reminder that in Scotland, unlike England, history isn't a tame thing confined to Telegraph supplements, but live and volatile. There are dates all over the place, from the Highland Clearances of the 19th century to Thatcher's 1988 Sermon on the Mound. You can be going about, minding your own business, when suddenly, bang! You've trodden on a smouldering remnant of Jacobitism or fallen through an unhealed Tory cut.

So maybe that's what this is about, the desire to get away from all that contaminated history. After all, if someone offered you the opportunity to make the world anew – no nuclear weapons, lots of new council houses, free prescriptions, free tuition, cheap green energy, stupendous wealth, oil, oil and more oil – wouldn't you take it?

Even so, the yes campaign has its weak spots. In November, the SNP's white paper outlined its vision for an independent Scotland. It filled in much of the detail – but left a lot out. What, for instance, will it cost to buy a whole new nation, and with what money will those bills be paid?

McLaren is dismissive of George Osborne's claim that an independent Scotland would need an alternative currency: "The Bank of England wants as many people as possible to use its currency. It's a business, and it's in its interest to let Scotland use the pound." And if it doesn't? "This is all the media keep asking. Why? It's silly. We know we're going to keep the pound. Ask us something interesting about what will happen after independence." But the money is interesting. "I don't agree, and most voters think it's boring, too. Can we not get on to why we actually want independence?"

OK, so why do you want it? "I don't like the fact that we can be taken into illegal wars when every one of our politicians voted against it. I don't like the way Britain portrays itself on the world stage. I think an independent Scotland would be a lot more peaceable and reasonable. I'd like to reform local authorities – they're too big, so we don't have local engagement. We spend too much on the army. And, God, it would be great to get rid of Trident.

"Mostly, I think often when something goes wrong, we go, oh, it's Westminster's fault. If we ran our own affairs, we'd make our own mistakes and find our own solutions. Of course we'd get it wrong, but we'd have ourselves to blame and no one else. It would be a healthier situation than this slightly childish democracy." So it's about growing up? "Yes." And have people taken on board that if you get it, you can't go back? "Yes. That's why people are taking it so seriously. They know this is it."

Euan Davidson, ­Liberal Democrat, voting no. Photograph: Robert Ormerod for the Guardian

On the Isle of Mull, 150 miles away, Iain Mackay looks after 7,000 acres of one of Scotland's most lucrative exports: scenery. Mull is beautiful and strange, and the light does funny things to your heart. At Torloisk on the western edge, Mackay has considerately scattered Highland cattle – so photogenic, so ginger – across the low ground.

The bigger picture is that it's bloody hard farming here. Thin soil, patchy grazing, extreme wind and rain. Mackay, 41, lives with his girlfriend in a caravan squelched into a corner of his farmyard. He's friendly and thoughtful, involved in both the Farming for Yes campaign and attempts to make it easier for young people to get into agriculture. "You feel very removed from power here," he says. "But in some ways that's an advantage: just leave us alone and let us get on with it."

Life on the islands is expensive. A tonne of hay costs £25 on the mainland; £60, with carriage charges, on Mull. "Rural areas in Scotland used to be Liberal or even Conservative with the landed classes. My grandparents have voted Conservative all their lives. But the SNP say Mrs Thatcher was the best thing that ever happened to them because of the way she treated Scotland."

How does he feel the campaign is going so far? "I was at a Highland cattle sale in February and an English chap came up. We usually get on well, but he was saying, 'We support you guys. Look at the money we give you.' I said, 'So why do you want to hold on to us? If we're costing you that much, let us go.' The other bits of the empire took back their independence a while ago and are doing fine."

Mackay's English farmer is unusual. Even the threat of losing 59 mainly Labour MPs from Westminster, thus opening up the possibility of an everlasting Tory majority, doesn't seem to trouble the English much. The most visible signs that anyone is paying attention are in business. Most large companies have contingency moving plans in place (though the SNP say they had the same plans before devolution and that never came to anything), and while property sales from Scots to Scots haven't been affected, the top end has slowed as English or overseas buyers wait and see.

"I'm saddened by all this stuff about separation," Mackay says, "as if we're going to take a chainsaw down the country and float off somewhere. We're supposed to be a union just now, and a union is supposed to be two people getting together to decide what's best for each other. At the moment, Scotland doesn't feel as if it's an equal."

Back in Edinburgh, Anya O'Shea, 23, is a seasoned Labour party member involved in the university's no campaign. She admits they're having trouble challenging the blissful picture presented by the pro-independence movement. "They can say, 'If you vote yes, there'll be no bedroom tax, no austerity measures, free tuition, you'll never have a Conservative government again.' We're arguing for the status quo, and that's not so easy. We've been promised more devolved powers after a no vote, but we can't tell people what those will be."

Out on the doorsteps of Leith or Granton, she finds votes usually divide according to age and sex: men yes, women no. And the newly enfranchised 16-year-olds are mainly no – they live in a global world, so why choose to make it smaller? "Young people always ask about job opportunities. They want to be able to move around, to go overseas. And older people, particularly if they work in the public sector, tend to say that they're voting no because they want job security."

O'Shea is a very British mixture: father Welsh, mother Polish, Irish ancestry, originally from London, Scottish boyfriend. "I'm British, but Scotland feels like home to me. I'm campaigning because this is so important, and part of a bigger picture. I don't want to feel as if I'm crossing a border when I go back down to London."

Like many others, she has picked up a couple of deeper faultlines in the debate. One, that not everyone has understood what powers Scotland already has under devolution. Two, that even the well-informed don't always grasp that a yes vote is not a vote for the SNP, but a vote to establish a whole new government with as many parties as it wants. Three, that very few people trust either politicians or the media to tell them the truth. "I've had friends say they're confused about the issues and ask where they can find a straightforward list of the pros and cons," O'Shea says. For the no campaign, that confusion is turning out to be an asset. As one Clydebank voter put it, "It's fear of the unknown that will keep Scotland united."

Far to the north, a plane is coming in over the sea. Nothing appears of the runway until, with only a few feet to go, the passengers find themselves looking down on a different land. Rocks and roads, a terminal, a few houses crouched low in the grass. The men – no women – who leave the plane carry bags marked Petrofac or Total. They wait for cars to take them to Lerwick, disjointed by the weekly 760-mile commute from London to Shetland.

They and 1,500 other workers are employed at the oil terminal at Sullom Voe or on the £800m construction site for the new gas plant nearby. At night, they come home to the huge "floatels" moored in the strip of water between Bressay and the mainland, ex-cruise ships or barges now used as accommodation blocks. One, known as the Zebra, has been painted in dazzling camouflage black-and-white. At night, it's lit up and sits rocking softly, staring at the town as the town stares back at it. One economy stapled on to another.

Shetland is a country within a country, a scale model of the referendum's main points. If this debate is all about oil, then here is where it starts and ends. Back in the 70s, Shetland cut a deal: in return for parking an oil terminal there, the industry would fund a charitable trust. At present, it holds about £217m – roughly £9,700 per person – which it spends on everything from folk festivals to bus services for the elderly. Salmond wants to do something similar for an independent Scotland.

The oil has been good in other ways. There are so many extra workers here now that the islands are experiencing a housing crisis. The few hotels around Lerwick are always full and, as there's little private accommodation to rent, prices for the few places available are up there with the London suburbs: £1,200 a month for a two-bed halfway out of town. There are 22,000 people in Shetland, no recession and less than 1% unemployment. "The only way you can be unemployed is if you don't want to work," one college student says.

Few in Shetland are voting for independence. Why would they? Many of the oil workers come from England or overseas and don't have a vote, the Union is working fine for them and, besides, most Shetlanders don't see themselves as Scots. This place has always considered itself closer kin to Norway than to Edinburgh or Westminster. As Lizzie Ratter, 29-year-old manager of Jamieson's knitwear shop in Lerwick puts it, "I'm a Shetlander first, a European second and a Scot not at all."

Ratter's grandmother used to knit the beautiful spidery Shetland shawls while walking round the island with a baby and the morning post on her back. Fish and knitting were the only way of surviving here, and as Shetland is still cut off from the mainland every winter, it doesn't see any point in relying on outsiders. Whether it runs out in 20 years or 40, most Shetlanders know that the oil won't last, the boom will end, and one day this will probably go back to being what it always was: a nation in miniature, looking out over the water.

In all the different Scotlands, one image always recurs: that of a marriage. Just for the sake of it, let's pretend that there's this couple, Albion and Caledonia. They've been married for a long time – more than 300 years – and it's been a productive but troubled relationship. Albion is happy with things as they are, but Caledonia wants to leave. Albion flirts with other countries and Caledonia feels bullied. When Caledonia threatens to walk out, Albion reminds her of all the things she'll lose: the house, furniture, money, security, music, pictures. Which only makes Caledonia more determined to go. Her blood is up, she's made plans, she's sure she'll get by somehow. All of us – English, Scottish, Welsh, Irish, whether we have a vote in the referendum or not – get to be counsellors on this. So what chance would you give them?

• This article was amended on 13 May 2014 to clarify that Roisin McLaren is president of the Edinburgh University Scottish Nationalist Association, and details of her family's political involvement.