Color correcting is where you take the flat D-Cinelike (or Log) profile, which should have no blown whites or crushed blacks and correct the muted color and shadows and contrast and make them appear as they should to your eyes. Color grading is where you first correct the color, and then change the look/feel to fit a certain mood that you want to portray. That is the short answer.
In my example, I was going for a more dramatic look and feel rather than have it look like it did in real life - it was cloudy and boring.
The "FILM" profiles appear to be attempts at Color Grading.
None and TrueColor profiles appear to be attempts at Correcting.