countdown vs counting

countdown and counting both are nouns.

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

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

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

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

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