Ok, understand that I am no expert. Here goes, a hydraulic camshaft is one designed for hydrualic liftes. Some lifters are solid chunks of metal. They require periodic adjustment (done on the rocker arm) but are very accurate in their action. There is no give in them. Many older hotrod engines will have a set of tall wing bolts holding the valve covers on, that is so the cover can be easily removed to adjust the rocker arms.
Hydrualic lifters have oil passages in them and require pressurized engine oil to "pump them up". With no oil, they collapse. Hydrualic lifters don't require any adjustment beyond the initial installation. They are usuaaly quieter because solid lifters can get out of adjustment and have some gap between the lifter and the pushrod and this causes some tapping noise.
Roller cams are designed for lifters that actually have a small roller at the end that contacts the camshaft lobe. Solid and hydraulic lifters have a flat bottom that rides directly on the cam lobe. Even with oil, there is a lot of friction caused by pressure on the lifter from the valve spring through the pushrod. It takes a certain amount of horespower to overcome this friction. The roller lifter with its built-in roller riding on the cam lobe has far less friction and therefore there is more horsepower for the rear tires. Also because of the roller's easy movement over the cam lobe, the lobe can have a sharper incline for a faster opening valve. This can create more accurate timing of the valve and allow for more power. Roller lifters require a bracket to keep the roller properly lined up on the lobe. Its a cylindrical roller, not a ball bearing so if the lifter should turn slightly in the lifter bore, the roller would no longer be aligned with the cam lobe and damage to the roller and cam lobe would result. If you see an engine with roller lifters opened up, you will see some metal bars connecting one lifter with the next nearest one. This keeps them aligned.
So when someone talks about a solid cam, they are actually refering to the type of lifter the cam is made to use. Same with a hydraulic cam or a roller cam.