detain vs lag

detain is not a noun while lag is a noun.

Word	Noun	Adjective	Verb	Adverb
detain	No	No	Yes	No
lag	Yes	No	Yes	No

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

detain (noun)	lag (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

detain (verb)	lag (verb)
cause to be slowed down or delayed	throw or pitch at a mark, as with coins
stop or halt	cover with lagging to prevent heat loss
deprive of freedom; take into confinement	hang (back) or fall (behind) in movement, progress, development, etc.
	lock up or confine, in or as in a jail