Figurative language is a broad category that includes figures of speech as well as sound devices and imagery. Figures of speech are words or groups of words that must be taken in a non-literal sense in order to understand their meaning. Examples of figures of speech are similes, metaphors, irony, synechdoche, allusions, puns, hyperbole, understatement, and personification. All of these use words in a non-literal, or figurative, way. 

Figurative language can also include wording that creates an image for the reader or that uses sound devices to add a deeper level of meaning to a word or group of words. Imagery is wording that evokes a five-senses response. Words such as "glittering," "screeching," "frigid," "lemony," and "smoky" create sensory reactions in the reader. Onomatopoeia, words that mimic the sounds they name, are a type of figurative language. Words such as "drip," "howl," "whiz," "tinkle," and "zip" are examples of onomatopoeia. Other sound devices such as alliteration, consonance, and assonance are also types of figurative language. Poetry especially takes advantage of such sound devices to create a mood or reinforce a meaning. For example, in these lines from "Stopping by Woods on a Snowy Evening," the repeated long /e/ sound reinforces the sweeping wind: "The only other sound’s the sweep
Of easy wind and downy flake."

So figures of speech fall into the broader category of figurative language, which includes words that are non-literal in their meanings as well as words that evoke sensory reactions in readers (imagery) or use sound devices to enhance the meaning of a phrase or sentence.

Figurative language and figures of speech are essentially the same thing, but we refer to it with two different terms. It is appropriate to say either when referring to any of the types of figures of speech or figurative language. Figurative language and figures of speech convey an implied or symbolic meaning rather than a literal meaning. This can be achieved through using one or more of the many types of figurative language. Some of the most common figures of speech are simile, metaphor, personification, symbolism, hyperbole, and idiom. 

Let's consider a simile and how it can convey meaning:

"She was as beautiful as a rose."

What is the meaning of this sentence? Is there literally a woman who has a very red face with many petals? Most likely not. This sentence and the use of simile works on the understanding that roses are a beautiful flower, perhaps inspiring wonder or admiration in the person who looks upon them. To call a woman as beautiful as a rose means that her appearance is on par with the appearance of a rose, possibly similarly inspiring admiration in the person who looks at her.