When we say “war poetry” today, the sort of writing that comes to mind is a conglomeration of Wilfred Owen, Siegfried Sassoon and the other great writers of the first world war. It means descriptions of mud, wire and slaughter on a horrific scale. It includes accusations that the top brass prolonged hostilities for no good reason and that people at home supported the cause in ignorance. It involves fierce protest as well as intense sympathy. It issues a warning.

Because poetry of this sort has been drip-fed into British schools for several generations (interestingly, the process did not start as soon as the war ended, but only began in earnest during the 1960s), it has settled in the public mind at an extraordinary depth. There are large benefits, of course. The best poetry of the first world war is exceptionally powerful – not just the lyrics of Owen and others, but the more complex and modernistic narrative of In Parenthesis by David Jones (which still has some claim to be considered a neglected masterpiece). Furthermore, by rubbing its readers’ noses in the brutal facts of conflict and suffering, it possibly creates a social value as well – by helping to educate people in the human cost of war, and in the process discouraging them from starting or supporting another one.

At the same time, maybe there are disadvantages. Perhaps by placing such an emphasis on war poetry in the school curriculum, we don’t actually put people off the idea of fighting, but inculcate the idea that it is somehow normal for the British to take up arms? Perhaps it solidifies the idea of us as a war-like nation? There is a literary consequence to the classroom focus too. By concentrating on the poetry of one conflict, which to an important extent is shaped by its particular circumstances, it directs attention away from the poetry of other wars.

Not just the poetry of other wars, in fact, but other kinds of war poetry. “I am the enemy you killed, my friend,” says the dead soldier encountered in Owen’s “Strange Meeting”: “I parried; but my hands were loath and cold”. This summarises the whole circumstance of first world war poetry: it often involved hand-to-hand fighting; it was intimate. The second world war, by contrast, was for many soldiers a more distanced affair. Keith Douglas when taking aim in his poem “How to Kill”, says: “Now in my dial of glass appears / the soldier who is going to die”. He still thinks of him as a fellow creature (the soldier “moves about in ways / his mother knows, habits of his”) but also feels a crucial separation – a gap that exists as a physical space, and proves the conflict has frozen or exterminated a part of the speaker’s own humanity.

The difference between these two poems is shorthand for the differences between two periods and two kinds of war poetry. It is also an opportunity to point out that while the Owen poem has been read by millions of schoolchildren in the last 50-odd years, the Douglas poem (which is just as good, if not better) has been read by a handful. By not conforming to the pattern of war poetry laid down between 1914 and 1918 (actually between about 1916 and 1918), it has been sidelined.

The contemporary American poet Yusef Komunyakaa, who has written poems about Vietnam. Photograph: James Keyser/Time & Life Pictures/Getty Image

The point here is not to discredit poetry of the first world war. As a collective act of witness, made at an extraordinary level of technical skill and with equally extraordinary emotional power, it is in its terrible way magnificent. The point, rather, is to say that our definition of “war poetry” has become too narrow to be accurate or fair. By extending it we are not only able to make a large literary gain – by admiring a much wider range of expertise, thoughtfulness and compassion – but also to appreciate in even more varied and detailed ways the effects of war.

This applies to the first world war itself, if we look away from the frontline and move to the home-front poetry of men in uniform such as Edward Thomas, or women waiting for them such as Eleanor Farjeon. Or to the extraordinary reports by nurses and other volunteers such as Helen Mackay, May Wedderburn Cannan and Margaret Postgate Cole. Or to the visceral and proto-existentialist poems and songs and chants of “Anonymous” (“I don’t want a bayonet up my arsehole, / I don’t want my bollocks shot away”).

A glance across the landscape of war poetry written after 1918 gives an even more dramatic sense of variety. The frontline (in north Africa, then France) brilliantly evoked by Douglas – in his poetry as well as his memoir Alamein to Zem Zem – is just a part of the large picture in which also appears Alun Lewis writing about soldierly boredom and nervous waiting during the second world war, and Dylan Thomas writing about the blitz – and, around them, international voices speaking with and through and over them: Nelly Sachs, Paul Celan, Anna Akhmatova and Tadeusz Różewicz.

As we come towards the present day, our sense of dilation becomes even greater. Not just in the sense that poets have made far-flung wars visible at home (Yusef Komunyakaa writing about Vietnam, for instance, or Brian Turner about Iraq), but also because the reporting of wars in the media has encouraged non-combatants to address the subject in greater numbers than ever before. This is a difficult business, since it is all too easy to get caught grandstanding, or parading sensitivities, or seeming to aggrandise oneself by associating with a grand subject. But when it is done well it produces poems that earn the right to sit besides those written by people in uniform: Tony Harrison’s “A Cold Coming”, for example, or James Fenton’s “Dead Soldiers”.

Before the first world war, war poetry since time immemorial (The Iliad) had been largely concerned to celebrate, commend, remember and, yes, grieve. Think of Lord Byron’s Assyrian, coming down like a wolf on the fold, or Sir John Moore in Charles Wolfe’s poem about the battle of Corunna. Since 1918, like war itself, the poetry of conflict has become a thing of infinite variety, describing apparently infinite tragedy. Yet for all this – which deserves more acknowledgment than it gets – something has stayed the same. The something Owen meant when he spoke about “the pity”.

• Ten War Poems, edited by Andrew Motion, is published by Candlestick.