pulse rate vs vital sign

pulse rate and vital sign both are nouns.

Word	Noun	Adjective	Verb	Adverb
pulse rate	Yes	No	No	No
vital sign	Yes	No	No	No

As nouns, vital sign is a hypernym of pulse rate; that is, vital sign is a word with a broader meaning than pulse rate:

pulse rate: the rate at which the heart beats; usually measured to obtain a quick evaluation of a person's health
vital sign: sign of life; usually an indicator of a person's general physical condition

Other hypernyms of pulse rate include rate.

pulse rate (noun)	vital sign (noun)
the rate at which the heart beats; usually measured to obtain a quick evaluation of a person's health	sign of life; usually an indicator of a person's general physical condition