number system vs numeration system

number system and numeration system both are nouns.

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

As nouns, number system and numeration system are synonyms defined as:

number system and numeration system: any notation for the representation of numbers

Other synonyms of number system include number representation system, system of numeration.

number system (noun)	numeration system (noun)
any notation for the representation of numbers	any notation for the representation of numbers