During the stress test, the heart is tested at a higher exercise level. Positive for ischemia is concluded from deviations of normal levels in certain parts of the ECG signal, as well as from other signals that the test person gives (for instance chest discomfort).
When ischemia does not occur in rest, an ECG / cardiogram (which is made in rest) will not show abnormalities.
In your case, there seems to occur ischemia during physical activity, but not in physical rest. This means that although you may be alright during most of the time, situations may occur when your heart really runs into trouble (physical activity, stress, cold weather or combinations of them). You need to avoid that, because it could easily end up in an infarction.
I.m.o. you need to go for the angiogram.
The angiogram will give a good view of the position and severity of blockages in your coronary arteries and in many cases, if problem areas are found, they can be stented immediately.