lower rank vs low status

lower rank and low status both are nouns.

Word	Noun	Adjective	Verb	Adverb
lower rank	Yes	No	No	No
low status	Yes	No	No	No

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

lower rank: the state of being inferior
low status: a position of inferior status; low in station or rank or fortune or estimation

Other hypernyms of lower rank include lowliness, lowness.

lower rank (noun)	low status (noun)
the state of being inferior	a position of inferior status; low in station or rank or fortune or estimation