I guess I’ve never seen any “official” explanation of Profiles. I learned this stuff a long time ago as I was playing with styles to set up one for my default templates as well as for image exports.
If your images are like like my 4th one, I would expect that the style you are using has Profiles turned off. The default Hidden Line is set up that way as are the others that are shown as “fast” styles by the addition of the green stopwatch icon.
Personally I prefer the working style to include profiles but with them set to 1 as in the last image in my previous post.
I did miss out another case in which Profiles are displayed. That is when a line drawn on a face doesn’t divide that face. That can be leveraged for display in some cases but it’s really a good trouble shooting tool. The line drawn across the top of the box in the foreground doesn’t go all the way across. The gap isn’t easily seen but if you were to try using something like Push/Pull on one side of the line, it would move the entire face of the box.
With Profiles turned on, you can see that edge shows as a profile. If it divided the larger face, it would show as a thin line.