fall back vs hang back

fall back and hang back both are verbs.

Word	Noun	Adjective	Verb	Adverb
fall back	No	No	Yes	No
hang back	No	No	Yes	No

As verbs, hang back is a hyponym of fall back; that is, hang back is a word with a more specific, narrower meaning than fall back:

fall back: hang (back) or fall (behind) in movement, progress, development, etc.
hang back: to lag or linger behind

Other hyponyms of fall back include drag, drop back, drop behind, get behind, trail.

fall back (verb)	hang back (verb)
go back to bad behavior	to lag or linger behind
retreat
hang (back) or fall (behind) in movement, progress, development, etc.
fall backwards and down
move back and away from
have recourse to