formal logic vs system of logic

formal logic and system of logic both are nouns.

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

As nouns, system of logic is a hypernym of formal logic; that is, system of logic is a word with a broader meaning than formal logic:

formal logic: any logical system that abstracts the form of statements away from their content in order to establish abstract criteria of consistency and validity
system of logic: a system of reasoning

Other hypernyms of formal logic include logic, logical system.

formal logic (noun)	system of logic (noun)
any logical system that abstracts the form of statements away from their content in order to establish abstract criteria of consistency and validity	a system of reasoning