time limit vs period of time

time limit and period of time both are nouns.

Word	Noun	Adjective	Verb	Adverb
time limit	Yes	No	No	No
period of time	Yes	No	No	No

As nouns, period of time is a hypernym of time limit; that is, period of time is a word with a broader meaning than time limit:

Other hypernyms of time limit include period, time period.

time limit (noun)	period of time (noun)
a time period within which something must be done or completed	an amount of time