library card vs borrower's card

library card and borrower's card both are nouns.

Word	Noun	Adjective	Verb	Adverb
library card	Yes	No	No	No
borrower's card	Yes	No	No	No

As nouns, library card and borrower's card are synonyms defined as:

library card and borrower's card: a card certifying the bearer's right to use the library

library card (noun)	borrower's card (noun)
a card certifying the bearer's right to use the library	a card certifying the bearer's right to use the library