"Adaptive cruise control" sounds like the vechicle is just controlling speed based on the car in front. It does not sound like it implies any type of auto-steering.

Yes, this is exactly what this does. "Lane assist" does the steering.

I think the good think that Tesla does though, is having a simpler package for all of that. German makers can't keep but making 5 different systems that you can (or not) combine so they can charge more $$$.