time of life vs time period

time of life and time period both are nouns.

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

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

time of life: a period of time during which a person is normally in a particular life state
time period: an amount of time

Other hypernyms of time of life include period, period of time.

time of life (noun)	time period (noun)
a period of time during which a person is normally in a particular life state	an amount of time