One of the first questions, one has to answer, when faced with the project of replacement or restoration, is 'What is it?'
Is it ceramic? Is it some sort of plaster or cement? Is it wood? Stone?
Identifying what a piece is made of, can sometimes be perplexing. If the piece is broken and you can see its interior, it helps in identifying.
Some soft clays can fool you into thinking it's plaster. Here are some tests, you can try out.
If the interior appears pure white, it might be plaster, it might be clay. If it's clay, it might be earthenware or it might be china or porcelain.
Test with the point of a Xacto blade, to see if it easily powders off. If it does, it's either plaster or very soft clay. If it's pure white, it's most likely plaster. If it has a slight pinkish hue, it could easily be mexican clay.
If it does not easily powder off, and is very hard, then it's either earthenware or porcelain. If it's shiney, even inside, then it's china. Porcelain will still have a dull appearance to broken edges.
So now, if its very hard but not shiney, then we're down to earthenware or porcelain. Tap the piece with the handle of your Xacto blade. Does it ring? Earthenware, depending on the size of the piece, might have a ring to it but it will not have the 'thin', high pitch as that of porcelain. Porcelain will have a high pitch and will last more than a quarter second, where as earthenware's ring is very short (time) and not as high pitch (tone). When testing for a ring, don't hold the piece. Set it on another hard surface, like a dinner plate or a metal turn table.
If still in doubt as to whether the piece is earthenware or porcelain, run the sharp point of your blade, along the broken edge. If absolutely no pieces, flake off, then it's porcelain.
Mexican clay will have a pinkish or slightly brown hue to it and will chip off easily. It has no ring.
Earthenware can sometimes fool you, as it can be colored. Usually white or red (terra cota). It has a slight ring to it when tapped, but short lived. Not very high pitched and has a 'thick' sound.
Porcelain also can be colored. Just about any color. It will not flake off, when you drag your blade across the broken edge. It has a high pitch sound and clear (not thick sounding) It appears very hard but not shiney.
China is unmatched by any clay. A broken edge is still shiney.
Stoneware (harder than earthenware clays), may have a slight shine to the broken edge but very visible coursely ground stone pieces. Very hard and does not flake off easily.
Plaster appears very white but when matched up with the white of china, it appears dull. It easily flakes off with a light drag of your blade. Much like chalk. Very chalky.
Another plaster, which is super hard, will still flake off but has a harder feel and appearance. Can be easily mistaken for mexican pottery.
Filled resins, can appear much the same as china but will have a hard plastic sound when tapped. These are clear resins mixed with things like plaster or other powdered chemicals. These are restored with yet more clear resin.
Any time you need a filler that is pure titanium white, you can actually purchase powdered titanium from a pottery supply.
Knowing what a piece is made of, helps you determined what materials you will need to repair or replace a piece.
All clays can be molded from a plaster mold. All resins and plasters, can be cast into a rubber mold.
If a piece is not broken but you can still see the interior, you can use the same way of testing. If the piece is not broken and you can't see the interior then you have to go by appearance and feel.
Again, the tapping to hear the ring, helps a lot. In addition, just the outward appearance can help. If it appears to be clay and has a bluish hue to the white background, it's china.
Porcelain can be just about any color. If it feels very hard, harder than clay, has a slight high pitch ring then it's probably porcelain.
If it has a ring but not very high pitch, it's probably poured clay (earthenware) Does it have a hole in the bottom? It's earthenware or stoneware.
Stoneware is rarely used for figurines (poured).
Resin, when tapped, has no ring and a definite plastic sound. Usually solid.
If I've overlooked anything, give me a holler here.