The first ICUs were created by anesthesiologists, but since then (1950s), anesthesiologists have made up an decreasing proportion of intensivists. Now, most intensivists are internal medicine trained. Out of about 1300 graduating anesthesia residents each year, only about 50 go into critical care. A similar number do trauma surgery/CCM. Compare that to about 500 pulm/CCM grads. Most often, anesthesia trained intensivists staff SICUs, although they can staff any adult ICU. The practice models vary, but many divide their time between OR and ICU. The exact ratio depends on the individual and the practice they're in.
A large part of anesthesiology is critical care in the OR. Even if a patient is health to begin with, with general anesthesia, we paralyze them (=respiratory failure), give them anesthetics (vasodilators and negative inotropes), and take away their protective reflexes. So if they weren't critical to begin with, they sure are under GETA. Add in multiple medical comorbidities and surgical pathology and you can see why it's a logical transition from OR to ICU.