There are primarily two types of aileron designs in GA airplanes. The first type you mentioned is the "differential" type where the up aileron has a greater displacement than the down aileron. The other type you referred to is known as "Frise" type ailerons. Both accomplish the same thing but in different ways.
As you know, when entering a turn you have to use coordinated rudder input. What happens if you don't use rudder? That's right, the nose of the airplane wants to move in the direction opposite the turn. This phenomena is commonly referred to as "adverse yaw". So to assist in correcting for adverse yaw, designers implement these two aileron types.
On the first type, the differential, the "up" aileron moves up farther than the "down" aileron moves down. When the "down" aileron moves down, it changes the chord of the wing and effectivley increases lift. This increase in lift also causes an increase in drag and the nose of the airplane wants to move in the direction opposite the turn. So, the up aileron causes some drag on that wing and helps, along with rudder, to keep the turn coordinated.
The "frise" type accomplish the same thing, but instead the leading edge of the "up" aileron drops below the bottom of the airfoil into the free stream of air and causes the drag which helps correct for adverse yaw. Good luck!
Regards