Dinnerware is a synonym, especially meaning a set of dishes, including serving pieces.
The broader term Tableware includes dishes, cutlery, and drinking vessels. Flatware refers to plates and cutlery. Hollowware refers to containers like bowls and pitchers, especially if made of metal.
Modern dishes may be made of earthenware, stoneware, porcelain, glass, and durable plastics, such as melamine resin. Disposable dishes made of paper or lightweight plastics may be used for casual eating. Historically, dishes have also been made of wood, metals such as pewter, and even animal skulls.
In British English the term crockery is used.