Shortness of breath means that you simply cannot get enough air to satisfy your body's craving for it. It stems from the injured heart muscle's lack of oxygen. It's different from simply being "winded" in that with being out of breath due to exertion, your need is gradually overcome by simply resting. With a heart attack, that doesn't happen. It literally can feel like it is impossible to get enough air.
In both cases I described, I was able to overcome the feeling simply by resting. There is a difference between the two, and I'm simply not able to find the right words to describe it. It might have to do with recovery time v.s. endurance. I understand the distinction you are making with a heart attack, in that resting does not alleviate the craving for air or oxygen. The symptom is persistent.
What experience do you have with pulmonary thrombosis? It's been ages since I've looked up anything about it on-line, but back in 1999 I read that it was a very commonly-missed diagnosis. In at least one case I know of (late wife), progressive blood obstructions from blood clots were misdiagnosed as pneumonia. I would think that a lung-capacity test should have indicated that something other than pneumonia was at work (since it would show normal, despite patient's shortness of breath). Do you know what's being done in that area?