library routine vs subroutine

library routine and subroutine both are nouns.

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

As nouns, subroutine is a hypernym of library routine; that is, subroutine is a word with a broader meaning than library routine:

Other hypernyms of library routine include function, procedure, routine, subprogram.

library routine (noun)	subroutine (noun)
a debugged routine that is maintained in a program library	a set sequence of steps, part of larger computer program