respiratory rate vs rate of respiration

respiratory rate and rate of respiration both are nouns.

Word	Noun	Adjective	Verb	Adverb
respiratory rate	Yes	No	No	No
rate of respiration	Yes	No	No	No

As nouns, respiratory rate and rate of respiration are synonyms defined as:

respiratory rate and rate of respiration: the rate at which a person inhales and exhales; usually measured to obtain a quick evaluation of a person's health

respiratory rate (noun)	rate of respiration (noun)
the rate at which a person inhales and exhales; usually measured to obtain a quick evaluation of a person's health	the rate at which a person inhales and exhales; usually measured to obtain a quick evaluation of a person's health