In the United States, they do the same fellowship. Some folks elect to only do thoracic surgery and some elect to limit their practice to cardiac surgery only. One would usually find this type of arrangement in larger academic centers. The majority of folks who do a Cardiothoracic fellowship will do both cardiac and thoracic.
At my institution, we have cardiac surgeons who do vascular surgery but no thoracic and thoracic surgeons who do no cardiac or vascular.