common sense vs horse sense

common sense and horse sense both are nouns.

Word	Noun	Adjective	Verb	Adverb
common sense	Yes	No	No	No
horse sense	Yes	No	No	No

As nouns, common sense and horse sense are synonyms defined as:

Other synonyms of common sense include good sense, gumption, mother wit, sense.

common sense (noun)	horse sense (noun)
sound practical judgment	sound practical judgment