muse vs puzzle

muse and puzzle both are nouns.

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

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

muse: reflect deeply on a subject
puzzle: be uncertain about; think about without fully understanding or being able to decide

muse (noun)	puzzle (noun)
the source of an artist's inspiration	a game that tests your ingenuity
	a particularly baffling problem that is said to have a correct solution

muse (verb)	puzzle (verb)
reflect deeply on a subject	be a mystery or bewildering to
	be uncertain about; think about without fully understanding or being able to decide