rate of payment vs payment rate

rate of payment and payment rate both are nouns.

Word	Noun	Adjective	Verb	Adverb
rate of payment	Yes	No	No	No
payment rate	Yes	No	No	No

As nouns, rate of payment and payment rate are synonyms defined as:

rate of payment and payment rate: the amount of money paid out per unit time

Other synonyms of rate of payment include installment rate, repayment rate.

rate of payment (noun)	payment rate (noun)
the amount of money paid out per unit time	the amount of money paid out per unit time