vaginal birth vs birthing

vaginal birth and birthing both are nouns.

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

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

vaginal birth: the parturition process in human beings; having a baby; the process of giving birth to a child
birthing: the process of giving birth

Other hypernyms of vaginal birth include birth, giving birth, parturition.

vaginal birth (noun)	birthing (noun)
the parturition process in human beings; having a baby; the process of giving birth to a child	the process of giving birth