There really is a huge, huge variety. I'm entering a peds critical care fellowship this summer, of which cardiac critical care is a huge portion. Even at the ICU level of care, there's a lot of potential directions to go. Some places, the Cardiac ICU's are very cardiologist driven, others they're the realm of the intensivists. After completing a cardiology fellowship, if the Cardiac ICU, with the post op hearts, myocarditis, ECMO, etc, is what lights your fires, you can complete a 4th year of fellowship in Cardiac Critical Care. More and more places are splitting their PICU's into separate Cardiac and general PICU's (see the construction projects at Seattle Children's or Children's Memorial in Chicago). Or if you're really crazy and want to do it all - PICU, CVICU, outpatient clinic - you can do a 5 year combined CCM/Cardiology fellowship and become board certified in both Critical Care and Cardiology.
In addition to the recognized 4th year fellowships in Interventional and Critical Care, there are also some options for further training in diagnostic and EP fields. Additionally, as mentioned, transplant is a major setting, and if you were interested in a med/peds sort of set up, you could also go into Adult Congenital Heart Disease management (which can also be entered from adult cardiology).