higher status vs higher rank

higher status and higher rank both are nouns.

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

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

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

Other synonyms of higher status include senior status, seniority.

higher status (noun)	higher rank (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