backache vs lumbar pain

backache and lumbar pain both are nouns.

Word	Noun	Adjective	Verb	Adverb
backache	Yes	No	No	No
lumbar pain	Yes	No	No	No

As nouns, lumbar pain is a hyponym of backache; that is, lumbar pain is a word with a more specific, narrower meaning than backache:

backache: an ache localized in the back
lumbar pain: backache affecting the lumbar region or lower back; can be caused by muscle strain or arthritis or vascular insufficiency or a ruptured intervertebral disc

Other hyponyms of backache include lumbago.

backache (noun)	lumbar pain (noun)
an ache localized in the back	backache affecting the lumbar region or lower back; can be caused by muscle strain or arthritis or vascular insufficiency or a ruptured intervertebral disc