social status vs social rank

social status and social rank both are nouns.

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

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

Other synonyms of social status include rank, social station.

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