An analogy draws a comparison between two disparate ideas, generally for the purpose of explaining an unusual or difficult-to-understand idea by relating it to a broadly familiar concept. While metaphors and similes are figures of speech, an analogy is an argument. Metaphors and similes often help develop an analogy.
“They crowded very close about him, with their hands always on him in a careful, caressing grip, as though all the while feeling him to make sure he was there. It was like men handling a fish which is still alive and may jump back into the water.”
In this excerpt from his essay “A Hanging,” George Orwell explains the interactions between the man about to be hanged and the prison guards around him by comparing this unusual situation to one that is more commonplace and easily understood—that of a fish out of water.
“The new snow was like powdered sugar.”
This is more precisely a simile and does not advance a logical argument.