day vs time period

day and time period both are nouns.

Word	Noun	Adjective	Verb	Adverb
day	Yes	No	No	No
time period	Yes	No	No	No

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

Other hypernyms of day include period, period of time.

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

day: the period of time taken by a particular planet (e.g. Mars) to make a complete rotation on its axis
time period: an amount of time

Other hypernyms of day include period, period of time.

day (noun)	time period (noun)
a period of opportunity	an amount of time
time for Earth to make a complete rotation on its axis
a day assigned to a particular purpose or observance
the time after sunrise and before sunset while it is light outside
a point or period in time
the recurring hours when you are not sleeping (especially those when you are working)
an era of existence or influence
the time for one complete rotation of the earth relative to a particular star, about 4 minutes shorter than a mean solar day
the period of time taken by a particular planet (e.g. Mars) to make a complete rotation on its axis