Sliding collision is typically like a player vs. wall collision. It allows the player to move parallel to the wall, but not perpendicular. It's called "sliding" collision because it's like "sliding along a wall", the key being that any motion parallel to the wall is kept, and the rest is discarded.
For a bullet type collision or "inelastic" collision (common in the old arcade games), you don't need to worry about anything else but whether there is a "hit" or overlap of the sprites. The sprites either stick together, or they explode or game-over or whatever.
For an "elastic" collision, you need to know about the shape of the two surfaces that are colliding, the direction the objects are moving, the mass, and velocity, etc., so that you can figure out how the motion of the objects will change. A good example of a game that might use elastic collision would be a pool game. Also, if you want realistic physics for say, vehicles in a 3D game, you would take elastic collision of the wheels with the ground into consideration in your motion equations.
There are probably more collision scenarios, like a mouse on an object, or a player passing through a region of water. They would all be handled differently than a "sliding collision".
Hope this helps...
Ed
