How might coronary heart disease affect the heart muscle and the circulatory system?

Directly. The coronary arteries and their branches carry the blood and oxygen to the heart muscle cells. Poor flow, low oxygen, cells die- equals heart attack. If enough muscle dies, then heart failure, cardiac arrest, no circulation, and death.
Coronary disease. It suggests that the blood flow to the heart muscle is impaired and the heart function in consequence is negatively impacted thus decreasing the functional capacity of the circulatory system.