active birth vs vaginal birth

active birth and vaginal birth both are nouns.

Word	Noun	Adjective	Verb	Adverb
active birth	Yes	No	No	No
vaginal birth	Yes	No	No	No

As nouns, vaginal birth is a hypernym of active birth; that is, vaginal birth is a word with a broader meaning than active birth:

active birth: childbirth during which the mother is encouraged to be an active participant
vaginal birth: the parturition process in human beings; having a baby; the process of giving birth to a child

Other hypernyms of active birth include accouchement, childbearing, childbirth.

active birth (noun)	vaginal birth (noun)
childbirth during which the mother is encouraged to be an active participant	the parturition process in human beings; having a baby; the process of giving birth to a child