logical system vs system of logic

logical system and system of logic both are nouns.

Word	Noun	Adjective	Verb	Adverb
logical system	Yes	No	No	No
system of logic	Yes	No	No	No

As nouns, logical system and system of logic are synonyms defined as:

Other synonyms of logical system include logic.

logical system (noun)	system of logic (noun)
a system of reasoning	a system of reasoning