time interval vs lag

time interval and lag both are nouns.

Word	Noun	Adjective	Verb	Adverb
time interval	Yes	No	No	No
lag	Yes	No	Yes	No

As nouns, lag is a hyponym of time interval; that is, lag is a word with a more specific, narrower meaning than time interval:

time interval (noun)	lag (noun)
a definite length of time marked off by two instants	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

time interval (verb)	lag (verb)
	throw or pitch at a mark, as with coins
	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