problem vs puzzle

problem and puzzle both are nouns.

Word	Noun	Adjective	Verb	Adverb
problem	Yes	No	No	No
puzzle	Yes	No	Yes	No

As nouns, puzzle is a hyponym of problem; that is, puzzle is a word with a more specific, narrower meaning than problem:

problem: a question raised for consideration or solution
puzzle: a particularly baffling problem that is said to have a correct solution

problem (noun)	puzzle (noun)
a source of difficulty	a game that tests your ingenuity
a question raised for consideration or solution	a particularly baffling problem that is said to have a correct solution
a state of difficulty that needs to be resolved

problem (verb)	puzzle (verb)
	be a mystery or bewildering to
	be uncertain about; think about without fully understanding or being able to decide