Aileron differential???
Of course not. That's akin to saying the pilot always pulls up to go up. What's up? Away from the ground or toward the aircraft canopy. If an aircraft is maintaining level flight upright, the lift vector is in the direction of the canopy. If it is flying inverted, the lift vector is toward the landing gear. And yes, the loads on the aircraft change dramatically when the attitude changes. The aerodynamic reactions also change. The basic lift and drag of the wing, for example, are effected by angle of attack which is, in part, a function of speed and attitude.
The only force that doesn't change is gravity x mass of craft (weight). All other forces change. That's how we change the path or speed of an object. By exerting forces upon it. Those changing forces are caused by thrust, lift, and drag.