higher rank vs higher status

higher rank and higher status both are nouns.

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

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

higher rank and higher status: higher rank than that of others especially by reason of longer service

Other synonyms of higher rank include senior status, seniority.

higher rank (noun)	higher status (noun)
higher rank than that of others especially by reason of longer service	higher rank than that of others especially by reason of longer service