nap vs slumber

nap and slumber both are nouns.

Word	Noun	Adjective	Verb	Adverb
nap	Yes	No	Yes	No
slumber	Yes	No	Yes	No

As verbs, slumber is a hypernym of nap; that is, slumber is a word with a broader meaning than nap:

Other hypernyms of nap include catch some Z's, kip, log Z's, sleep.

nap (noun)	slumber (noun)
sleeping for a short period of time (usually not in bed)	a dormant or quiescent state
a card game similar to whist; usually played for stakes	a natural and periodic state of rest during which consciousness of the world is suspended
the yarn (as in a rug or velvet or corduroy) that stands up from the weave
a soft or fuzzy surface texture
a period of time spent sleeping

nap (verb)	slumber (verb)
take a siesta	be asleep