youth vs time of life

youth and time of life both are nouns.

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

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

youth: the time of life between childhood and maturity
time of life: a period of time during which a person is normally in a particular life state

youth (noun)	time of life (noun)
the freshness and vitality characteristic of a young person	a period of time during which a person is normally in a particular life state
young people collectively
a young person (especially a young man or boy)
early maturity; the state of being young or immature or inexperienced
the time of life between childhood and maturity
an early period of development