recursive routine vs subprogram

recursive routine and subprogram both are nouns.

Word	Noun	Adjective	Verb	Adverb
recursive routine	Yes	No	No	No
subprogram	Yes	No	No	No

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

Other hypernyms of recursive routine include function, procedure, routine, subroutine.

recursive routine (noun)	subprogram (noun)
a routine that can call itself	a set sequence of steps, part of larger computer program