I've always referred to it as the "Center of Pressure". The concept makes more sense when viewed as a cross section.
Hmmm, that could be identical to what is called the aerodynamic cneter but it doesn't have to. In fact usually it isn't.
The pitching moment in the aerodynamic center doesn't have to be Zero.
The trick is the pitching moment remains constant even if Alpha (or Lift being a function of Alpha) changes.
Center of pressure would be the point where the pitching moment is Zero for a given Alpha. If Alpha changes the pitching moment around this point will change, i.e. the center of pressure will move.