It was easier in the good old days. If a piece of writing had metre and rhyme and things like that it was obviously a poem.
But even then there were people like Blake and Whitman who said they were writing poems while discarding most of poetry's identifying marks.
My rule of thumb is "if the writer says it's a poem then that's what it is."
But calling it a poem doesn't necessarily mean that it's any good. Most poetry is bad.
Virginia Woolf was clearly exercised by the problem. A relative asked her why she didn't write poems and she said she found prose rhythms more interesting and challenging.
But I'm sure there were times when she wondered if she wasn't a poet after all.
The Waves (which I'm reading at the moment)is a long prose poem. It has the density, the verbal sprightliness we associate with poetry. It aims for beauty.
She pursues the debate in the book. Bernard is a novelist; he knows a lot of things but his vision is fuzzy. Louis and Neville are poets; they know fewer things than Bernard but their vision is sharp. Can we derive a universal law from this perception? I doubt it.
According to Woolf's law, Browning would be reclassified as a novelist. This is suggestive, but I don't see that it gets us very far.
At the beginning of his Oxford Book of English Verse (published in the early 1930s) W.B. Yeats printed a piece of prose by Walter Pater as if it were verse. It was a turning point. A recognition that the old distinctions had become meaningless.
Poetry is dead. Prose is dead. From now on there is only Writing.