chew over vs puzzle

chew over is not a noun while puzzle is a noun.

Word	Noun	Adjective	Verb	Adverb
chew over	No	No	Yes	No
puzzle	Yes	No	Yes	No

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

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

chew over (noun)	puzzle (noun)
	a game that tests your ingenuity
	a particularly baffling problem that is said to have a correct solution

chew over (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