cut price vs bargain rate

cut price and bargain rate both are nouns.

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

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

Other synonyms of cut price include cheapness, cut rate.

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