Type - Main function - Common uses -
Sliding clamps - Linear clamping - Fixtures, assembly, welding.
Quick release clamps - Quick locking/unlocking - Woodworking, CNC, assembly.
Horizontal clamps - Quick clamps with horizontal handle - Fixtures where the handle should lie flat.
What all three have in common is that they save time, provide repeatable clamping and reduce the risk of the workpiece moving during machining or assembly.