Angina is an equivalent of a muscle cramp, meaning there is low blood flow, but there isn't complete block of flow. The cells are starving for oxygen and nutrients during that time but they aren't dying or getting damaged because angina is mostly felt during exertion and it resolves with resting. A heart attack is the most extreme type of blood flow limitation where the muscle cells arent' getting any blood flow and they are beginning to die. This usually occurs at rest and typically implies complete or nearly complete blockage.
By definition a spasm is a temporary constricton of the vessel and may not cause heart cell damage, but if I understand the question is there damage in the long term with a significant occlusion that causes angina? And if left untreated for a sufficient period of time can it cause damage or death (infarction) of heart muscle tissue?.
For another perspective the coronary obstruction theory does not adequately explain all the observed facts concerning myocardial infractions.
For instance the major etiologic (cause and effect) factor in an MI is a destructive chemical process; specifically, in situations of stress on the myocardial (heart muscle) tissue, often as a result of small vessel disease, the myocardial tissue gets insufficient oxygen and nutrients. This leads to destructive lactic acidosis in the tissue which, if unchecked, leads to death of the myocardial cells. This process is largely unrelated to coronary artery disease.
As the doctor states, angina is caused when blood flow to an area of the heart is decreased. This impairs the delivery of oxygen and vital nutrients to the heart muscle cells. But when this happens, the heart muscle must use alternative, less efficient forms of fuel so that it can perform its function of pumping blood to the body. The byproduct of using this less efficient fuel is a compound called lactic acid that builds up in the muscle and causes pain. This leads to destructive lactic acidosis in the tissue which, if unchecked, leads to death of the myocardial cells.
Also, I postulate that that heart cells are not uniformally of sufficient degree of vulnerbility or lack there of. Lack of oxygenated blood may for a short period of time effect some heart cells within the cell group of the tissue effected with a shortage of blood supply causing some more vulnerable cells to die more quickly than the other more healthy cells. Can't rule out a spasm could cause cell damage.