differences between parable and poem

No. A parable can be, and usually is rendered in prose. Poems, however, usually (but not always) are rendered in a specific meter, a rhythm which one can hear while reading the poem aloud. Modern poetry has often dispensed with meter, but nevertheless, the standards of expression (as in the use of simile, metaphor and figurative language) are much less rigorous in poetry than in prose. In prose, lucidity and logical expression are highly valued. In poetry, the quality of the imagery and the emotional impact on the reader are paramount.

Comparing poetry to parables is actually an exercise in comparing apples to boulders. These are not even remotely related exercises. A parable seeks to illustrate a philosophical, or moral or religious "truth" through a simple story. In fact, a parable may be delivered in poetic form. Probably the best example of this are the fables of Jean de la Fontaine. He wrote fables, which were, in essence, parables about human nature (the characters of his fables, however, were usually animals). He wrote them in a very structured verse.

So, while a parable may be rendered in verse, and therefore be considered poetry, there really is no relationship between parables and poetry. La Fontaine was an exception, i believe it is correct to say that the majority of parables are rendered in prose