countdown vs reckoning

countdown and reckoning both are nouns.

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

As nouns, reckoning is a hypernym of countdown; that is, reckoning 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)
reckoning: the act of counting; reciting numbers in ascending order

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

countdown (noun)	reckoning (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
	problem solving that involves numbers or quantities
	a bill for an amount due