numeration vs counting

numeration and counting both are nouns.

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

As nouns, numeration and counting are synonyms defined as:

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

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

numeration (noun)	counting (noun)
the act of counting; reciting numbers in ascending order	the act of counting; reciting numbers in ascending order
naming numbers