Brake Assist (BAS) is used because in an emergency some drivers brake too timidly and do not apply maximum pressure.
BAS recognizes emergency braking and automatically ensures full pressure is applied.

Electronic stability programme.
When a car under-steers the front threatens to plough straight. With ESP the rear wheel is slowed to bring the car back on car back on course.

If a car over-steers through a corner its because the rear wheels have lost grip.
ESP slows the front wheel allowing the driver to regain control.