number system vs unary

number system and unary both are nouns.

Word	Noun	Adjective	Verb	Adverb
number system	Yes	No	No	No
unary	Yes	Yes	No	No

As nouns, unary is a hyponym of number system; that is, unary is a word with a more specific, narrower meaning than number system:

number system: any notation for the representation of numbers
unary: the bijective base-1 numeral system: in order to represent a number N, an arbitrarily chosen symbol representing 1 is repeated N times.

Other hyponyms of number system include positional notation, positional representation system, unary numeral system.

number system (noun)	unary (noun)
any notation for the representation of numbers	the bijective base-1 numeral system: in order to represent a number N, an arbitrarily chosen symbol representing 1 is repeated N times.

number system (adjective)	unary (adjective)
	consisting of or involving a single element or component