China is commonly used to mean all crockery or dinnerware. But the term really has stricter meaning.

Ceramics just mean "made from clay".

Fine china or porcelain is made from feldspar, flint,and kaolin clay, a fine white clay. These materials are fired at extremely high temperatures to form a non porous ceramic. It is extremely hard.

Fine china is translucent which means that if you hold a dinner plate up to the light and pass your hand behind it, you should be able to see a your hand's shadow. It should also give a good "ring" sound if you flick it.

Cheaper "china" is made with cheaper clay and fired at lower temperatures so it is less strong. It does have the advantage of allowing stronger colours to hold.

Bone china is a variation of fine china which includes bone ash to intensify whiteness and is more translucent.

Stoneware is fired at the very high temperature and has a strength and durability close to china ware. It also has good thermal and shock resistant properties so it is very robust. Much oven-to-tableware is made from stoneware. Again, because of the high temperatiure, the colours used tend to be less rich and vivid and more "earthy"

Terracotta does, quite literally mean baked earth. It traditionally has a low temperature fired red clay body which can be glazed or unglazed.

Earthenware is made from less fine clay and is always slightly porous even when glzed.

Ironstone is a stronger kind of Earthenware made from better quality clay and fired at higher temperatures.