day vs period of time

day and period of time both are nouns.

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

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

Other hypernyms of day include period, time period.

As nouns, period of time is a hypernym of day; that is, period of time 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
period of time: an amount of time

Other hypernyms of day include period, time period.

day (noun)	period of time (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