numeration vs nosecount

numeration and nosecount both are nouns.

Word	Noun	Adjective	Verb	Adverb
numeration	Yes	No	No	No
nosecount	Yes	No	No	No

As nouns, nosecount is a hyponym of numeration; that is, nosecount is a word with a more specific, narrower meaning than numeration:

Other hyponyms of numeration include blood count, census, nose count, countdown, miscount, poll, recount, sperm count.

numeration (noun)	nosecount (noun)
the act of counting; reciting numbers in ascending order	a periodic count of the population
naming numbers