Suppose I have two cameras, c1 and c2, observing the same scene. I can now

1. Calibrate each camera independently (e.g., with MATLAB's Camera Calibration App)
2. Calibrate both cameras simultaneously (e.g., with MATLAB's Stereo Camera Calibration App).

Interestingly, the values calculated for the intrinsic parameters of both cameras are different using method 1) and method 2). To me it is not clear why this should be the case. The intrinsic parameters of camera 1 are independent of the ones of camera 2 and vice versa, why should they influence each other? I suppose there is some form of optimization aiming to optimize simultaneously in the stereo case, however I would think that the "stereo optimum" is the same as the combined "single optimum".

Any insight?