Vermeil is made of real silver that is covered with a layer of real gold. In the U.S., to be considered vermeil, a piece has to be coated with gold that is at least 10 karats pure.
Gold plating refers to a thin layer of gold that covers the surface of a metal core – which can be made of a variety of non-gold metals (typically cheaper metals like brass).
The most notable difference between vermeil and gold-plated pieces is in the metals that make up their base. Gold vermeil, or just vermeil, should always be made with real silver as the base metal – otherwise, the piece cannot be sold as vermeil.
Vermeil pieces are generally more expensive than gold-plated ones. Part of the reason for this is that vermeil jewelry is made with real silver, whereas many gold-plated pieces are made with cheaper metals that are used to create the core under the plating.