lawsuit vs legal proceeding

lawsuit and legal proceeding both are nouns.

Word	Noun	Adjective	Verb	Adverb
lawsuit	Yes	No	No	No
legal proceeding	Yes	No	No	No

As nouns, legal proceeding is a hypernym of lawsuit; that is, legal proceeding is a word with a broader meaning than lawsuit:

lawsuit: a comprehensive term for any proceeding in a court of law whereby an individual seeks a legal remedy
legal proceeding: (law) the institution of a sequence of steps by which legal judgments are invoked

Other hypernyms of lawsuit include proceeding, proceedings.

lawsuit (noun)	legal proceeding (noun)
a comprehensive term for any proceeding in a court of law whereby an individual seeks a legal remedy	(law) the institution of a sequence of steps by which legal judgments are invoked