A curveball will spin foward. The top spin on the ball sends it down.
A slider spins to the pitchers glove side. This will cause the ball to move to the pitchers glove side. (The ball does also drop too)
An easy way to think of it is this: the ball will follow the direction it's spinning in.
If the ball has top spin [spinning fowards], it drops.
If the ball is spinning clockwise, it moves left.
If the ball spins counter clock wise, it moves to the right.