A number of years ago I won a prize for a prose poem. Since then I have been asked every now and then what the distinction is between poetic prose and a prose poem, and how you can tell the difference. I remind the questioner that (in modern times) the prose poem began as a poem that rebelled against the strictures of form in much the same way as free verse did. With both of these, the main difference from conventional poetry is in the presentation.
A prose poem should first of all be a poem; it should use language to do what poems do. It can, and should, use poetic devices that are not acceptable in simple prose. An extended metaphor may be the underlying conceit. The use of meter, of repetition, of internal rhyme - all the tools employed by the poet only enhance the prose poem.
Try taking a formal (shaped) poem and present it as prose: "Let me not to the marriage of true minds admit impediments. Love is not love which alters when it alteration finds, or bends with the remover to remove." Shakespeare's sonnet remains just that, no matter the presentation.
In my own work, I often develop a poem/idea in paragraph form, throwing in everything that I want to say and often twice. Then I look for places the piece can be broken into sections or stanzas. After that, I tackle each stanza separately, honing it down to what needs to be expressed in the best way I can express it, always with a sense of the whole. Only after that do I take a look at it and consider form. Would certain restrictions enhance the poem? If I present it as free verse, will the subtleties of rhythm be lost? Different questions for different presentations. Even going back to the prose poem is considered.
All that thought goes into the formation of each poem. That's why poetry is not simply inspiration, it is a learned and practised craft.