lag vs hang back

lag is a noun but hang back is not a noun.

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

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

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

lag (noun)	hang back (noun)
the act of slowing down or falling behind
one of several thin slats of wood forming the sides of a barrel or bucket
the time between one event, process, or period and another

lag (verb)	hang back (verb)
throw or pitch at a mark, as with coins	to lag or linger behind
cover with lagging to prevent heat loss
hang (back) or fall (behind) in movement, progress, development, etc.
lock up or confine, in or as in a jail