Color correction is when you adjust the subtle differences in color, white balance, and exposure between various shots to make them more unified. For example, if you have two different shots taken hours apart, but in the finished product those shots are all a part of one scene, then you’d obviously want the lighting and color to match. So in post, you tweak it until you’ve achieved consistency between shots.
The term color grading tends to apply to the extra effects added to the shot in post that may create a more stylized look. For instance, if you’re shooting a scary movie, you might adjust the coloration of a given scene to accentuate the cooler colors i.e., greens, blues, and purples. Additionally, you might darken the exposure to create a very foreboding feel.