The lifters have rollers on the bottom, so they roll on the camshaft. Flat Tappet engines don't have rollers on the lifters, so they just slide metal to metal.
Yes, we have roller motors. A hydraulic roller has a roller on it, and a flat tapped it does not. The term "solid" does not refer to it not having a roller. A solid lifter does not use oil pressure to automatically adjust height.
As already stated, roller (or hydraulic roller) engines refers to the type of lifter being used, hydraulic roller or flat tappet. Rollers are more recent tech than flat tappet. Here's a nice link showing the benefits of roller vs flat tappet:
Just read that one recently myself. Roller blocks have taller lifter bores. Putting roller lifters in a non-roller block requires special lifters (which are very expensive). Unless one has a compelling reason to keep a non-roller block (restoring a classic and you want the original engine, etc) it's usually cheaper to find a roller block from a junkyard and sell the old block.