childbearing vs birthing

childbearing and birthing both are nouns.

Word	Noun	Adjective	Verb	Adverb
childbearing	Yes	Yes	No	No
birthing	Yes	No	No	No

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

childbearing: 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 childbearing include birth, giving birth, parturition.

childbearing (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

childbearing (adjective)	birthing (adjective)
relating to or suitable for childbirth