lottery vs numbers pool

lottery and numbers pool both are nouns.

Word	Noun	Adjective	Verb	Adverb
lottery	Yes	No	No	No
numbers pool	Yes	No	No	No

As nouns, numbers pool is a hyponym of lottery; that is, numbers pool is a word with a more specific, narrower meaning than lottery:

lottery: players buy (or are given) chances and prizes are distributed by casting lots
numbers pool: an illegal daily lottery

Other hyponyms of lottery include tombola, lucky dip, numbers, numbers game, numbers racket, raffle, sweepstakes.

lottery (noun)	numbers pool (noun)
players buy (or are given) chances and prizes are distributed by casting lots	an illegal daily lottery
something that is regarded as a chance event