puzzle vs problem

puzzle and problem both are nouns.

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

As nouns, problem is a hypernym of puzzle; that is, problem is a word with a broader meaning than puzzle:

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

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

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