With Proof Colors off, Photoshop uses the document’s normal color management and the working space set in Edit > Color Settings, under Working Spaces. Which working profile applies depends on the image type: typically RGB for color photos and Gray for black-and-white images. CMYK and Spot are generally not relevant for most photography work.

“Monitor RGB” proofing is different: it simulates sending the image directly to the monitor’s RGB space, which is why it can look different from the normal Photoshop display. So the normal view is not simply “system color profile only”; it is Photoshop’s managed display based on the document/working space, while proofing can simulate a different output condition.