mull over vs puzzle

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

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

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

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

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

mull 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