program library vs subroutine library

program library and subroutine library both are nouns.

Word	Noun	Adjective	Verb	Adverb
program library	Yes	No	No	No
subroutine library	Yes	No	No	No

As nouns, program library and subroutine library are synonyms defined as:

program library and subroutine library: (computing) a collection of standard programs and subroutines that are stored and available for immediate use

Other synonyms of program library include library.

program library (noun)	subroutine library (noun)
(computing) a collection of standard programs and subroutines that are stored and available for immediate use	(computing) a collection of standard programs and subroutines that are stored and available for immediate use