action at law vs proceeding

action at law and proceeding both are nouns.

Word	Noun	Adjective	Verb	Adverb
action at law	Yes	No	No	No
proceeding	Yes	No	No	No

As nouns, proceeding is a hypernym of action at law; that is, proceeding is a word with a broader meaning than action at law:

action at law: a judicial proceeding brought by one party against another; one party prosecutes another for a wrong done or for protection of a right or for prevention of a wrong
proceeding: (law) the institution of a sequence of steps by which legal judgments are invoked

Other hypernyms of action at law include legal proceeding, proceedings.

action at law (noun)	proceeding (noun)
a judicial proceeding brought by one party against another; one party prosecutes another for a wrong done or for protection of a right or for prevention of a wrong	(law) the institution of a sequence of steps by which legal judgments are invoked