base rate vs rate of interest

base rate and rate of interest both are nouns.

Word	Noun	Adjective	Verb	Adverb
base rate	Yes	No	No	No
rate of interest	Yes	No	No	No

As nouns, rate of interest is a hypernym of base rate; that is, rate of interest is a word with a broader meaning than base rate:

base rate: the interest rate set by the Bank of England for lending to other banks
rate of interest: the percentage of a sum of money charged for its use

Other hypernyms of base rate include interest rate.

base rate (noun)	rate of interest (noun)
the interest rate set by the Bank of England for lending to other banks	the percentage of a sum of money charged for its use