social rank vs status

social rank and status both are nouns.

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

As nouns, status is a hypernym of social rank; that is, status is a word with a broader meaning than social rank:

social rank: position in a social hierarchy
status: the relative position or standing of things or especially persons in a society

Other hypernyms of social rank include position.

social rank (noun)	status (noun)
position in a social hierarchy	the relative position or standing of things or especially persons in a society
	a state at a particular time