sperm count vs counting

sperm count and counting both are nouns.

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

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

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

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

sperm count (noun)	counting (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