It's sounds like you're talking about adaptive cruise control. That is totally separate from automatic emergency braking. My adaptive cruise control has stop/start functionality, which brings the car to a complete stop and starts it back up, as long as there is a car in front of me to bounce the radar off of. But, that is not automatic emergency braking, which will apply the brakes if you are about to crash into something. It works whether or not your cruise control is activated
I have no idea what it is called. I know I can set one of three distances I want to follow behind a car and if that car slows down it slows me down. Also if a car stops or slows way down to make a turn it will suddenly apply the brakes and wait for the car to turn. When it does this it is sudden and gives me a jerk. So I would say it is automatic emergency braking so I don't hit the car.