elapsed time vs period of time

elapsed time and period of time both are nouns.

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

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

Other hypernyms of elapsed time include period, time period.

elapsed time (noun)	period of time (noun)
the time that elapses while some event is occurring	an amount of time