sperm count vs enumeration

sperm count and enumeration both are nouns.

Word	Noun	Adjective	Verb	Adverb
sperm count	Yes	No	No	No
enumeration	Yes	No	No	No

As nouns, enumeration is a hypernym of sperm count; that is, enumeration is a word with a broader meaning than sperm count:

sperm count: the act of estimating the number of spermatozoa in an ejaculate
enumeration: the act of counting; reciting numbers in ascending order

Other hypernyms of sperm count include count, counting, numeration, reckoning, tally.

sperm count (noun)	enumeration (noun)
the act of estimating the number of spermatozoa in an ejaculate	the act of counting; reciting numbers in ascending order
the number of sperm in an ejaculate	a numbered list