The fundamental difference between comprise and compose has to do with the whole versus the parts of any object or concept.
Let’s take a closer look at the definitions to put this in context: comprise is a verb that means “to include or contain” or “to consist of” as in, "The pie comprises 8 slices."
Compose means “to be or constitute a part of element of” or “to make up or form the basis of,” as in, "Eight slices compose the pie." The key rule to remember is that the whole comprises the elements or parts, and the elements or parts compose the whole.
Comprise means "contain", as in The hotel comprises 150 rooms. In other words, the hotel has or contains 150 rooms for guests. When you use "comprise", you’re talking about all the parts that make up something whole.
The similar-sounding word compose means "make up" as in Many ethnic groups compose our nation.
So, the parts compose the whole, but the whole comprises the parts.
Strict grammarians will never use "comprised of" in a sentence as it's not considered correct, just as "contained of" would be incorrect.
Incorrect: The United States is comprised of fifty states.
Correct: The United States comprises fifty states.