They can all be related, it really depends on the severity of one type over the other sometimes.

Limited blood flow can affect the nerves & muscles.
Nerve impingements can affect the signals sent to the muscles & vascular system.
Kind of a what came first..but they are intertwined most times.

Mainly most of the testing is to make sure there is nothing obvious or anatomical that is causing your TOS symptoms. And to rule out other reasons or other conditions.

If nothing obvious shows on all those tests , depending on the severity of sx & pain, surgery may or may not be the preferred course of action.

Each person has to figure out what will be best for them in the long run.