Here’s how I explained it to my eighth graders:
The subject is figurative language, which includes: similes, metaphors, irony, symbolism, hyperbole, apostrophe, and a few other items which I can’t recall off the top of my head.
A simile is a direct comparison. This is like that. He is as [blank] as a [blank]. You mention both things as being similar to one another.
A metaphor is an implicit comparison. Implicit because you don’t say “this is like that,” you say “this IS *.” For instance, I could say “Life’s a bitch.” That’s a metaphor. It is not, however, literally true. You could not, for instance, take a picture of someone’s life and end up with a portrait of a female dog. A metaphor is a kind of code. You substitute one thing for another, but you tell the reader exactly what you’re doing. Sometimes, you can get an extended metaphor, where you tell the reader once what you’re doing, and then keep the idea up without repeating the key to the code. For instance: My English teacher’s a real witch. I bet she rides a broom to class every day.
A symbol is similar to a metaphor in that it’s a code. The trick is, though, that the author doesn’t give you the key to the code. You have to figure it out for yourself. In To Kill a Mockingbird, Atticus Finch tells his daughter not to shoot her pellet gun at any mockingbirds, because it’s a sin to kill a mockingbird. The mockingbird becomes a symbol for Tom Robins (?) - and it could be argued vice-versa - because it represents destroying an innocent, a thing that did no harm. The author never comes right out and says “Tom is the mockingbird”. You have to figure it out for yourself.