What does it mean if the Electronic Stability Control light stays on while driving the car?

If the ESC light is on for an extended period while driving, it could mean a system malfunction or you have disabled the system. First, check whether you have disabled it, and switch it on. If the system is enabled and the light is on, there is a malfunction, and you must get it fixed as soon as possible.
Are ESP and ESC two different safety features?

No, Electronic Stability Program and Electronic Stability Control are the same safety features. They are different terms used by car manufacturers. The primary role and function of the system remain the same.
Is it safe to drive my car with ESC off?

It depends on your driving style and road conditions. It is safe to drive with ESC off if you are driving defensively and the road conditions are good with predictable traction. But if you drive on curvy roads with unpredictable traction, then it may not be a wise option to switch off the stability control. We recommend you not turn off the stability control when you drive as the roads are always unpredictable.
Does ESC prevent the vehicle from rolling over?

No. The stability control can only prevent the car from skidding when cornering. It can detect understeer or oversteer and assist the driver in correcting the mistake. If the vehicle spins out of control, it may roll over depending on the vehicle's speed.