childbirth vs giving birth

childbirth and giving birth both are nouns.

Word	Noun	Adjective	Verb	Adverb
childbirth	Yes	No	No	No
giving birth	Yes	No	No	No

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

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

Other hypernyms of childbirth include birth, birthing, parturition.

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