bargain rate vs cut price

bargain rate and cut price both are nouns.

Word	Noun	Adjective	Verb	Adverb
bargain rate	Yes	No	No	No
cut price	Yes	No	No	No

As nouns, bargain rate and cut price are synonyms defined as:

Other synonyms of bargain rate include cheapness, cut rate.

bargain rate (noun)	cut price (noun)
a price below the standard price	a price below the standard price