childbed vs birthing

childbed and birthing both are nouns.

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

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

childbed: concluding state of pregnancy; from the onset of contractions to the birth of a child
birthing: the process of giving birth

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

childbed (noun)	birthing (noun)
concluding state of pregnancy; from the onset of contractions to the birth of a child	the process of giving birth