A metaphor compares two things by making one thing assume all the characteristics of the other. For instance: "The sea is a hungry dog." In this line, the sea takes on all the attributes of a hungry dog. A metaphor is a complete comparison, and writers use it to make their expression new and stylized. Metaphorical language is most commonly used in poetry where the language is condensed and expression has to be exact and brief. Using metaphors helps poets express themselves in new and exciting ways.
Figurative language is language which uses figurative devices such as metaphors, similes and personification. Literally, the word "figurative" means giving a shape to a word, or seeing it in the form of a figure. To give an unusual or interesting shape to a thought means employing figurative language. For instance, a rose as a symbol of love or the Grim Reaper as a symbol of death (also an example of personification). Figurative language makes writing and reading more imaginative.
The words "figurative" and "metaphorical" both extend our visual and emotive understanding of a thing or an idea. We may not have expected the sea to be compared to a hungry dog, but the poet James Reeves (see Reference 3) used the metaphor and made us imagine the sea as ravenous and violent but also playful. The extensive use of metaphors and comparisons makes the poem a figurative one -- the literal image of a "sea" is taken and transformed into a figurative image of it in the form of a dog.
Essentially both figurative and metaphorical expressions use unlikely comparisons. Whereas a metaphor has a specific definition, however, figurative language is more extended. It includes many types of comparisons and analogies and also involves sound devices like alliteration, onomatopoeia and sibilance (see Reference 1). When the overall writing is shaped in a way that it refreshes the imagination with extended metaphors, unusual similes and personifications, we call that writing "figurative."