ABS is an abbreviation standing for Anti-Lock Braking System. It is included in the making of a car to assist the driver gain greater control of the car especially when braking.
When you press hard on the normal brake pedal, the disc/drum brakes are engaged and they slow you down. But at the risk of locking up the wheels. This means they do not have any circular movement left and due to the inertia of the car, they will just keep skidding along the road surface. Turning the steering wheel will have no effect as the wheels have very little grip left.
What the ABS does is monitor the wheels under braking. If the system senses that the wheels are about to stop moving, it releases the brake even if you are pressing the brake pedal. When the wheels are moving, you have enough grip on the road so you can turn the steering to give direction to your car.
EBD is an abbreviation standing for Electronic Brakeforce Distribution.
This system monitors each of the individual brakes and wheels. Under braking, it decides which wheel to brake more and which to brake less depending on many conditions like road friction (less priority) and body weight (higher priority) of the car.
Typically most of the braking force is distributed to the front, as the front is heavier than the rear half of the car.
In a few systems, immediately after braking, more pressure is applied on rear brakes before the effects of weight transfer become apparent and then the brake force is redistributed.