What apps benefits from monitor calibration?

It seems that a calibrated monitor benefits two types of software in different ways:

(1) non color managed apps, any software that displays photos including the browser, photo viewer, windows explorer…

(2) photoshop. The same photo displayed by the OS or in a browser looks slighly different when displayed in photoshop.

So, just exactly how does monitor calibration affect each of the software above? I know by experiment that color cast is remove, and grayscale is more linear. I believe photoshop also remaps color to make them more accurate so that the same photo displayed by photoshop on one machine should look identical to the same photo displayed by photoshop on another machine (both calibrated of course).

I’m trying to get a conceptual understanding of what goes on in monitor calibration.