formal logic vs logical system

formal logic and logical system both are nouns.

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

As nouns, logical system is a hypernym of formal logic; that is, logical system 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
logical system: a system of reasoning

Other hypernyms of formal logic include logic, system of logic.

formal logic (noun)	logical system (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