Setting aside the issue of technical differences, in everyday English, we would use this terms in this order: 1) pottery 2) ceramics 3) porcelain with (1) being the 'roughest' and (3) being the finest/most delicate.

Ceramics are what you get when you heat clay to a very high temperature and then cool it. If you add minerals to the clay before making ceramics, you get porcelain. The range of raw materials used to make pottery are wider than ceramics, and the temperature reached when heating is lower. Just for reference.