Many people confuse analogies, similes, and metaphors. Let me help.
Analogies compare things so that you can see a relationship between them. There are many ways to do it, but the key thing is that you compare in a way that gets you thinking about what things both things may have in common.
Similes do this by saying something is “like” or “as” something else.
He’s like a wall.
She’s as smart as a whip.
Her temper was like a storm.
Metaphors do this by saying something “is” something else.
That test was murder.
The company was a sinking ship.
The campaign is a dumpster fire.
So, analogies are comparisons, and metaphors and similes are two ways to make them.