I was confused about this until I took a course in metal clay. Metal clay is the generic term for metal powders mixed with a binder, which can be fired like clay and the binder burns off, leaving the metal. It can replace casting for some uses.
PMC (Precious Metal Clay) is one of the two major brands of metal clay. The other is Art Clay. Both groups make a variety of clay, and there are other sources of metal clay, too. Right now, the bornze clay must be fired in a metal container, embedded in charcol (to keep oxygen away from the metal). New clays are being developed and the old ones are coming out in forms easier to use. With the price in in precious metals, the base metal clays such as copper and bronze are very attractive. I happen to think that bronze is one of the most beautiful metals and bronze clay takes on various patinas when fired, including a rainbow patina.
It's fun to experiment with. You need a kiln, but very few tools and accessories, and it doesn't take up much space. I keep everything I need to work with (except my kiln_ in a tote bag and on a tray, so I can set up in the diningroom and work for a few hours, then put it away.
Right now I'm working with bronze clay, but I'll try the new copper clay soon. Silver clay seems to be the standard, and most courses are for work with silver clay.
I've attached a photo of a 20 inch necklace, with a toggle closing and charm (non-ceph) to give you an idea of what can be done.
Nancy