An antique is something that is dated 20 plus years. It can be trace dated to a certain date. Vintage on the other hand is a style from a era. for example the style of clothing from the 50s automobiles of the 30s etc...
Antique is older than vintage. 1990s clothes are old-fashioned, out of style; '60s-'80s clothes are vintage; '40s clothes are antique. Don't take that too precisely, but I think it's something like that.
Automobiles are 25 years. You can purchase a "antique" license plate at the BMV once your vehicle is 25 years old.