Poetry comes first - because poetry is in essence mnemonic language: language made easy to remember.
This is achieved in three ways: regular and repeated rhythm, rhyme and alliteration.
1. Rhythm - essentially chanting.
Rhythm can be divided in terms of either a few heavy beats, like nursery rhymes which often have two beats in a line but variable numbers of syllables and clusters of syllables; like
Sally go round the sun
Sally go round the moon
Sally go round the chim-er-ney pots
On a Saturday afternoon
(of course the above example also rhymes)
or in short patterns of stresses (metres) - like the
ti-tum ti-tum ti-tum ti-TUM
ti-tum ti-tum ti-TUM
of 'common metre'.
Quite of lot of the most famous English verse (Shakespeare, Milton, Wordsworth) is 'blank verse' which is (mostly) ti-tum all the way - generally avoiding alliteration and (especially) rhyme
Example from Shakepeare's Merchant of Venice, which has five ti-tums per line (iambic pentameter):
The quality of mercy is not strain'd,
It droppeth as the gentle rain from heav'n
Upon the place beneath: it is twice blest;
It blesseth him that gives and him that takes
Beats and stresses both make it easier to remember language - which is why all chanting (even of disorganized mobs) tends to be organized by beats and/ or stresses.
2. Rhyme - obviously. 'Nuff said.
3. Alliteration - in which the beginnings of words, or their most stressed syllables, are similar. This is almost obsolete and unappreciated - but was standard for Old English and most Middle English verse - especially when it was orally performed.
Here is an Old English pastiche by C.S Lewis (which Tolkien found defective) - the rule is half lines, two stresses in each half line falling on the alliterated sound and at least one alliteration common to the half lines: T, B, S, E, G and the 'ess' sound.
We were talking of dragons, Tolkien and I
In a Berkshire bar. The big workman
Who had sat silent and sucked his pipe
All the evening, from his empty mug
With gleaming eye glanced towards us:
"I seen 'em myself!" he said fiercely.”
Prose eschews regular rhythm, rhymes and alliteration but is made memorable by narrative, by telling a story.
Of course poetry can tell a story; and indeed poetry which tells a story - an epic or romance, for example - is the most memorable of all literary forms (probably the earliest formal language) - the characteristic production of 'bards', 'minstrels' and 'ballad singers'.
What this means is that some things that get called poetry are not essentially so, but only so by lineal descent: e.g. poetry based on syllable counting, or 'free verse'
- these are more of a 'high art' commentary on essential poetry - indeed free verse, in particular, is often subversive of essential poetry - and rigorously avoids any mnemonic aids such as regular rhythm, alliteration or rhyme.
(Yes, I know this is almost all of what gets called poetry nowadays - but that only goes to show...)
And prose which does not tell a story (like this essay) is not essentially prose.
THUS cometh the focus of poetry on specific words and images (stock images - such as the Kennings of Old English poetry - whale-road = sea; or poetic cliches such as the 'wine dark sea' from Homer);
and in prose the focus is on sense, on (detachable) message: meaning, morals, stock characters and stock situations (the prohibition which is always broken, the youngest son, the rule of three)...
There we have it: the essence of poetry, the essence of prose...