Porcelain is a type of ceramic clay. Another type is known as stoneware clay. Both have roughly the same ingredients except porcelain is pure white because it does not have iron and other oxides that would make it darker. If they’re formulated to be fired at similar temperatures, they can both be fired at together in the same kiln.
You can use porcelain and stoneware ceramic pots for cooking only in an oven. You have to be careful because extreme changes in temperature will cause them to crack so you can’t put a frozen pot into a hot oven, or put a hot pot into a freezer. Putting a ceramic pot on a stove top will also result in cracking because the part touching the hot burner will expand more than the top.