Very similar terms. Ceramics are anything made of fired clay. Could be pots and bowls, could be insulators or engine parts. Pottery are dishes made of ceramic. Sometimes other household items like candleholders might be called pottery, but not often. Pottery means the ceramic material, or the items made of it, but usually only dishes.are called pottery. China is another term for the same tthing, from a day when the best ceramics came from China. Usually it means white or light colored pottery, often porcelain. A common term is 'fine china': "We always get out the fine china for holiday meals." Porcelain is a particualr kind of clay used for making dishes. It is white and very fine and strong, and slightly translucent- you can see the glow of light through it faintly.

You should write 'china' instead of 'China' when talking about porcelain. To distinguish it from the country (中国). Another explicit word would be 'chinaware' or 'bone china' (white as bone?). While 'earthenware' is made from 'potter's clay'. And there is another form: 'celadon' (青瓷). With a grey/green (or grey/blue) glaze on earthenware, later on porcelain. Fashionable from Song to early Ming.

http://en.wikipedia.org/wiki/Porcelain http://en.wikipedia.org/wiki/Ceramics http://en.wikipedia.org/wiki/Pottery http://en.wikipedia.org/wiki/Bone_china