sense of hearing vs auditory sense

sense of hearing and auditory sense both are nouns.

Word	Noun	Adjective	Verb	Adverb
sense of hearing	Yes	No	No	No
auditory sense	Yes	No	No	No

As nouns, sense of hearing and auditory sense are synonyms defined as:

sense of hearing and auditory sense: the ability to hear; the auditory faculty

Other synonyms of sense of hearing include audition, auditory modality, hearing.

sense of hearing (noun)	auditory sense (noun)
the ability to hear; the auditory faculty	the ability to hear; the auditory faculty