Is heart enlargement the same thing as cardiomegaly?

No. In general, cardiac enlargement is defined as a local or widespread enlargement of the heart itself, resulting in an increase in the extent of the cardiac shadow that may be evident on imaging, suggesting local or widespread pathological changes in the myocardium.
The immediate pathological cause of cardiac enlargement is compensatory versus decompensated cardiac hypertrophy, but in a small percentage of patients, the immediate cause of cardiac enlargement is a cardiac effusion or tumour, so cardiac enlargement and cardiac hypertrophy are not exactly equivalent.