The Occupy London movement is marking its first month this week. It is routinely described as anti-capitalist, but this label is highly misleading. As I found out when I gave a lecture at its Tent City University last weekend, many of its participants are not against capitalism. They just want it better regulated so that it benefits the greatest possible majority.

But even accepting that the label accurately describes some participants in the movement, what does being anti-capitalist actually mean?

Many Americans, for example, consider countries like France and Sweden to be socialist or anti-capitalist – yet, were their 19th-century ancestors able to time-travel to today, they would almost certainly have called today's US socialist. They would have been shocked to find that their beloved country had decided to punish industry and enterprise with a progressive income tax. To their horror, they would also see that children had been deprived of the freedom to work and adults "the liberty of working as long as [they] wished", as the US supreme court put it in 1905 when ruling unconstitutional a New York state act limiting the working hours of bakers to 10 hours a day. What is capitalist, and thus anti-capitalist, it seems, depends on who you are.

Many institutions that most of us regard as the foundation stones of capitalism were not introduced until the mid-19th century, because they had been seen as undermining capitalism. Adam Smith opposed limited liability companies and Herbert Spencer objected to the central bank, both on the grounds that these institutions dulled market incentives by putting upper limits to investment risk. The same argument was made against the bankruptcy law.

Since the mid-19th century, many measures that were widely regarded as anti-capitalist when first introduced – such as the progressive income tax, the welfare state, child labour regulation and the eight-hour day – have become integral parts of capitalism today.

Capitalism has also evolved in very different ways across countries. They may all be capitalist in that they are predominantly run on the basis of private property and profit motives, but beyond that they are organised very differently.

In Japan interlocking share ownership among friendly enterprises, which once accounted for over 50% of all listed shares and still accounts for around 30%, makes hostile takeover very difficult. This has enabled Japanese companies to invest with a much longer time horizon than their British or American counterparts.

Japanese companies provide lifetime employment for their core workers (accounting for about a third of the workforce), thereby creating strong worker loyalty. They also give the workers a relatively large say in the management of the production process, thus tapping their creative powers. There are heavy regulations in the agricultural and retail sectors against large firms, which complement the weak welfare state by preserving small shops and farms.

German capitalism is as different from the American or British version as Japanese capitalism, but in other ways. Like Japan, Germany gives a relatively big input to workers in the running of a company, but in a collectivist way through the co-determination system, in which worker representation on the supervisory board allows them to have a say in key corporate matters (such as plant closure and takeovers), rather than giving a greater stake in the company to workers as individuals, as in the Japanese system.

Thus, while Japanese companies are protected from hostile takeovers by friendly companies (through interlocking shareholding), German companies are protected by their workers (through co-determination).

Even supposedly similar varieties of capitalism, for example Swedish and German, have important differences. German workers are represented through the co-determination system and through industry-level trade unions, while Swedish workers are represented by a centralised trade union (the Swedish Trade Union Confederation), which engages in centralised wage bargaining with the centralised employers' association (the Confederation of Swedish Enterprise).

Unlike in Germany, where concentrated corporate ownership has been deliberately destroyed, Sweden has arguably the most concentrated corporate ownership in the world. One family – the Wallenbergs – possesses controlling stakes (usually defined as over 20% of voting shares) in most of the key companies in the Swedish economy, including ABB, Ericsson, Electrolux, Saab, SEB and SKF. Some estimate that the Wallenberg companies produce a third of Swedish national output. Despite this, Sweden has built one of the most egalitarian societies in the world because of its large, and largely effective, welfare state.

And then there are hybrids that defy definition: China, with its large socialist legacy, is an obvious case, but Singapore is another, even more interesting, example. Singapore is usually touted as the model student of free-market capitalism, given its free-trade policy and welcoming attitude towards multinational companies. Yet in other ways it is a very socialist country. All land is owned by the government, 85% of housing is supplied by the government-owned housing corporation, and a staggering 22% of national output is produced by state-owned enterprises. (The international average is around 10%.) Would you say that Singapore is capitalist or socialist?

When it is so diverse, criticising capitalism is not very meaningful. What you have to change to improve the Swedish or the Japanese capitalist systems is very different from what you should do for the British one.

In Britain, as already physically identified by the Occupy movement, it is clear the key reforms should be made in the City of London. The fact that the Occupy movement does not have an agreed list of reforms should not be used as an excuse not to engage with it. I'm told there is an economics committee working on it and, more importantly, there are already many financial reform proposals floating around, often supported by very "establishment" figures like Adair Turner, the Financial Services Authority chairman, George Soros, the Open Society Foundations chairman, and Andy Haldane, the Bank of England's executive director for financial stability.

By labelling the Occupy movement "anti-capitalist", those who do not want reforms have been able to avoid the real debate. This has to stop. It is time we use the Occupy movement as the catalyst for a serious debate on alternative institutional arrangements that will make British (or for that matter, any other) capitalism better for the majority of people.