I have done a lot of research and I have found out that different planes have different climb angles. Some look like they are climbing at a higher rate than others. Why is this? Do some aircraft have higher or lower critical AoA than the other? If yes, then why? Is it the design of the airfoil?
If an airplane is pitched up 12° from the horizon, but climbing at 10°, then its angle of attack is only 2°.
The angle of attack doesn't have anything to do with climb performance. The maximum rate of climb and angle of climb are (mostly) determined by the amount of thrust the engine is creating, the efficiency of the wing, and the weight of the plane.
Different airfoil designs will indeed have different critical AoAs.