Why is there a difference between aileron upwards and downwards deflection angles?
You're correct that the ailerons are deflected differently when they are deflected up or down. This is done in order to counter the adverse yaw effect which occurs when ailerons are deployed. Consider the situation when the ailerons are deployed.



Image from aerospaceweb.org

One aileron is deflected downward while the other is deflected upward. One the side with the downward-deflected aileron, lift increases as the deflection effectively increases the camber of that portion of the wing. The opposite happens in the other side.

However, the drag is also affected by aileron deflection- both induced and profile drags. For same deflection, the profile drag increase is same in both the wings. However, the induced drag on both sides are not equal, with a larger amount the wing with the down aileron (as the lift is more and induced drag is proportional to the square of lift).

One way of overcoming this is to deflect the ailerons differentially, i.e. deflect the down aileron by a lesser amount than the up aileron. The following table shows the aileron deflection in a number of aircraft, which shows the differential aileron deflection ($\delta_{A}$ is the aileron deflection, in degrees).



Table from Aircraft Design: A Systems Engineering Approach by Mohammad Sadraey

This adverse yaw can also be prevented by the use of,


Frise ailerons
Use of spoilers (in the wing up aileron)
Cross coupled controls (rudder and ailerons).


There is another reason to use a differential aileron- to prevent tip stall at high angles of attack (stall speeds). The rolling couple on the aircraft is always the difference in lift between the two wings. At or near stalling speeds, it is better to reduce the lift in up-going aileron than increase it in down moving one and risk stalling it.