The heart is a muscular pump which is pumping 5-6 l of blood per minute. To be able to operate on the structures inside it, it has to be stopped. We all know that if the heart stops, all organs of the body would be depleted of oxygen and the person would not survive. For this reason the patient is put on temporary artificial heart lung machine(called cardiopulmonary bypass). The function of the heart is taken over by the machine as the blood from the heart is diverted into the machine. The heart can now be stopped. It is now empty and can be cut open to perform the surgical procedure. This is open heart surgery.
Bypass surgery on the other hand is performed on arteries of the heart. These arteries can be seen on the outside of the heart. There is no need to cut open the heart. Technically speaking, bypass surgery is not open heart surgery. Previously heart kung machine was used to perform bypass surgery, but now bypass surgery can be done on the beating heart.