A figure of speech is using language or words in ways that are beyond their literal interpretation. There are typically 10 figures of speech that are used as poetic devices.
Poetic devices include the way words rhyme, sound in lines of poetry together, and create rhythm when spoken. Poetic devices are used to arrange the words in ways that squeeze them for all of their meaning. Poetic devices of rhyme, rhythm and alliteration can set the mood of a poem.
Simile, Metaphor, Allegory, Onomatopoeia, Personification, Irony, and hyperbole are the most common figures of speech that are used as poetic devices. The links below contain all figures of speech and examples.
The poem is the most compressed form of the language, and so symbolism and comparisons must be used to squeeze as much meaning as possible out of each word chosen to be in the poem.
Interesting question. Don't quote me on this but I have always thought that figurative language is a term used for language that is based on some sort of comparison. Therefore under this heading you have similes, metaphors and personification. A figure of speech is thus language in which one thing is compared to something that seems to be entirely different. A figure of speech is never literally true, but a good figure of speech always surprises us with its comparison because it suggests a powerful truth.
Poetic devices is a much more general term for any "device" in poetry, including figurative language but also including devices such as alliteration, onomatopoeia, assonance etc. That is what I have always thought, anyway...