I think the term has been used for various capabilities over the years.
My friend's 10-year-old Toyota will chirp annoyingly if you drift over a lane line but that's all it does. It doesn't have any ability to steer the car back into the center of the lane. Is that "lane keeping"?
Mine has either off, warn, or warn+adjust (but adjustment is very gentle, more of a nudge).
I can imagine it can save a life someone dozing off and drifting.
No, that's "lane departure warning"