old-age pension vs retirement check

old-age pension and retirement check both are nouns.

Word	Noun	Adjective	Verb	Adverb
old-age pension	Yes	No	No	No
retirement check	Yes	No	No	No

As nouns, old-age pension and retirement check are synonyms defined as:

old-age pension and retirement check: a monthly payment made to someone who is retired from work

Other synonyms of old-age pension include retirement benefit, retirement fund, retirement pension, superannuation.

old-age pension (noun)	retirement check (noun)
a monthly payment made to someone who is retired from work	a monthly payment made to someone who is retired from work