Heart disease implies that something is not healthy in the heart muscle itself or in some other part of the cardiovascular system - the arteries and veins that carry the blood pumped by the heart throughout the body.
Cardiomyopathy refers specifically to disease of the heart muscle. If the rhythm with which the heart beats is impaired, the body (including the heart) will be affected by the irregular supply of oxygen to the cells and the accumulation of wastes in the blood not removed efficiently. As long as the effects of the cardiomyopathy go unresolved, the body continues to function in an impaired condition. As the body systems work harder to compensate for the effects of the particular disease condition, the reserves of strength and energy in the system are exhausted and not replenished.