lumbar pain vs backache

lumbar pain and backache both are nouns.

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

As nouns, backache is a hypernym of lumbar pain; that is, backache is a word with a broader meaning than lumbar pain:

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
backache: an ache localized in the back

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