The meanings of archaic and antiquated largely overlap; however, archaic implies having the character or characteristics of a much earlier time.

// the play used archaic language to convey a sense of period

The words antique and antiquated can be used in similar contexts, but antique applies to what has come down from a former or ancient time.

// collected antique Chippendale furniture

Some common synonyms of antiquated are ancient, antique, archaic, obsolete, old, and venerable. While all these words mean "having come into existence or use in the more or less distant past," antiquated implies being discredited or outmoded or otherwise inappropriate to the present time.

// antiquated teaching methods