cut rate vs cut price

cut rate and cut price both are nouns.

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

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

Other synonyms of cut rate include bargain rate, cheapness.

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