numeration vs countdown

numeration and countdown both are nouns.

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

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

numeration: the act of counting; reciting numbers in ascending order
countdown: counting backward from an arbitrary number to indicate the time remaining before some event (such as launching a space vehicle)

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

numeration (noun)	countdown (noun)
the act of counting; reciting numbers in ascending order	counting backward from an arbitrary number to indicate the time remaining before some event (such as launching a space vehicle)
naming numbers