What's the difference between a story and a poem

[milo]

A story poem is one that develops a central theme i.e. it usually has a beginning, middle and an end and can be written both in free verse and rhyme. In general terms the emphasis is on communicating with the reader so the delivery tends to be kept in the range of the understanding of the average reader’s vocabulary; why would you want to read a story holding a dictionary in your hands or scrambling your brain trying figure out what the writer was attempting to convey.

I stress this is a generalization and with all generalizations there will be a degree of overlapping, for example the English poet Phillip Larkin.
Poetry hacks have the insatiable need to graft their own perception on a poets work to place him/her into a convenient box for their understanding but with Larkin they can’t agree on whether he was a modernist writer or not.
Larkin’s friend, the Poet Laureate John Betjaman, a quintessential English poet, was definitely not a modernist and much of his poetry could fall easily in the story mould.

Of the two, Betjaman was by far the most popular poet with the general public, so it follows that writing in a style and manner to engage a wider audience who don’t give a toss about the nuts and bolts of writing poetry (Not that Betjaman didn’t) it gives the writer a broader appeal though it won’t bring you many accolades from the poetry elite.

Personally I admire both for different reasons. Larkin, a confirmed atheist who felt, when in a church alone to be compelled to-- take off my cycle-clips in awkward reverence.
Betjaman for the last two lines of this verse.

And Nurse came in with the tea-things
Breast high 'mid the stands and chairs-
But Nurse was alone with her own little soul,
And the things were alone with theirs.

But as they say—beauty lies in the eye of the beholder.

The two subsets are identified as the "lyric" and the "narrative"

Betjaman strongly favoured the lyric over the narrative but, possibly, your reading has more strongly favoured his narrative stuff. Larkin dealt almost exclusively with the lyric.