grammatical rule vs rule of grammar

grammatical rule and rule of grammar both are nouns.

Word	Noun	Adjective	Verb	Adverb
grammatical rule	Yes	No	No	No
rule of grammar	Yes	No	No	No

As nouns, grammatical rule and rule of grammar are synonyms defined as:

grammatical rule and rule of grammar: a linguistic rule for the syntax of grammatical utterances

grammatical rule (noun)	rule of grammar (noun)
a linguistic rule for the syntax of grammatical utterances	a linguistic rule for the syntax of grammatical utterances