pace vs rate

pace and rate both are nouns.

Word	Noun	Adjective	Verb	Adverb
pace	Yes	No	Yes	No
rate	Yes	No	Yes	No

As nouns, pace and rate are synonyms defined as:

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

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

pace (noun)	rate (noun)
a step in walking or running	the relative speed of progress or change
the relative speed of progress or change	amount of a charge or payment relative to some basis
a unit of length equal to 3 feet; defined as 91.44 centimeters; originally taken to be the average length of a stride	a quantity or amount or measure considered as a proportion of another quantity or amount or measure
the distance covered by a step	a magnitude or frequency relative to a time unit
the rate of moving (especially walking or running)
the rate of some repeating event

pace (verb)	rate (verb)
measure (distances) by pacing	assign a rank or rating to
regulate or set the pace of	estimate the value of
walk with slow or fast paces	be worthy of or have a certain rating
go at a pace