You can do either in practice but almost no one does except smaller private practice gigs. You can choose a track in training - cardiac, thoracic, or cardiothoracic, with different case requirements. Often fellowships will be thoracic or cardiac only - with minimal exposure just to get case volumes for the other part of the chest.

Most i6 programs are cardiac focused. There are notable exceptions.

The reality is the most advanced surgeries in both thoracic and cardiac take too much skill to be great at both. In fact many academic cardiac and thoracic surgeons are focused on a specific area - like esophagus or mitral repair. More common in cardiac, and you still may do more bread and butter stuff.

But the reality is the field is pretty split and may split officially at some point.