Same with Hyundai except they call them "Lane Keeping Assist" (LKA) and "Lane Following Assist" (LFA) and I have trouble remembering which one centers you and which one just keeps you from leaving the lane.
To me just based on the names I'd have expected keeping to be the one that actively positions you (it keeps you centered) and following to the one that just reacts when you are going to depart the lane (it keeps you following the lane).
Mostly now I just remember that the one that comes on automatically any time I'm going 40+ mph is the reactive one, and the one that I have to explicitly turn on is the centering one (although both come on automatically on certain highways based on data from the navigation system).