social rank vs social status

social rank and social status both are nouns.

Word	Noun	Adjective	Verb	Adverb
social rank	Yes	No	No	No
social status	Yes	No	No	No

As nouns, social rank and social status are synonyms defined as:

Other synonyms of social rank include rank, social station.

social rank (noun)	social status (noun)
position in a social hierarchy	position in a social hierarchy