enumeration vs counting

enumeration and counting both are nouns.

Word	Noun	Adjective	Verb	Adverb
enumeration	Yes	No	No	No
counting	Yes	No	No	No

As nouns, enumeration and counting are synonyms defined as:

enumeration and counting: the act of counting; reciting numbers in ascending order

Other synonyms of enumeration include count, numeration, reckoning, tally.

enumeration (noun)	counting (noun)
the act of counting; reciting numbers in ascending order	the act of counting; reciting numbers in ascending order
a numbered list