Are all V8 engine mounts solid? Are there any other types?

I'm not sure I understand what you mean by solid.

Stock engine mounts are rubber and steel.
There were a couple different designs, depending on the year, the later ones have the rubber bushing part surrounded by a steel shell, so even if the rubber could give way the engine is still secured.

What most people refer to as solid mounts are just steel mounts, that hold the engine solidly to the frame. They were never stock.

Are all V8 engine mounts solid? Are there any other types?
There are typically three kinds of motor mounts: stock (rubber), poly and solid. In the poly, the stock rubber insert is replaced with polyurethane. It's a stiffer material that allows less movement but transmits more vibration. The solid mount is just a piece of steel that replaces the whole clamshell piece. Obviously, there is even more vibration when you run solid mounts.