rate vs rate of payment

rate and rate of payment both are nouns.

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

As nouns, rate of payment is a hyponym of rate; that is, rate of payment is a word with a more specific, narrower meaning than rate:

rate (noun)	rate of payment (noun)
the relative speed of progress or change	the amount of money paid out per unit time
amount of a charge or payment relative to some basis
a quantity or amount or measure considered as a proportion of another quantity or amount or measure
a magnitude or frequency relative to a time unit

rate (verb)	rate of payment (verb)
assign a rank or rating to
estimate the value of
be worthy of or have a certain rating