Practitioners in critical care medicine are called intensivists. There are a few different routes to get to certification in critical care. Medicine offers both a 2 year critical care medicine fellowship (about 20 programs) and a 3 yr Pulmonary/Critical Care medicine fellowship (more common) which incorporates both pulmonology and critical care certifications. Certification can also be acheived w/ 1 yr CCM training by specialists in nephrology, neurology, GI, Cards, etc. Some hospitalists choose to get extra training in critical care but most are only board certified in internal medicine. Medicine trained intensivists tend to treat the sickest of the sick ICU patients, usually with numerous pre/comorbid conditions, metabolic derangements. Medicine training programs that incorporate significant ICU training (such as the one I am in) tend to produce more well qualified hospitalists. Some hospitalist years do exist, but formal board certification, to my knowledge, is not available yet. In some places, hospitalists and internists follow their patients in the ICU, often dictating care and may get a CCM consult for difficult cases. This is the "open ICU" arrangement. A "closed ICU" is usually where an intensivist assumes control of patient care during the ICU admission. Most recent literature suggests that the closed ICU is frankly superior to the open ICU setup and the outcomes are improved when CCM trained docs are employed.
Via anaesthesia, one can do a 1-2 year critical care fellowship generally geared towards PACU and SICU care. Sick patients, but often with better protoplasm than the average MICU patient. Employment demand for ICU trained anaesthesiologist is relatively low primarily because they lack the surgical training of the trauma/CCM guys.
Via surgery, there is critical care and trauma/critical care fellowships. These are geared towards trauma, burns and other patients with surgical needs. Patients tend to be younger, with less comorbid conditions. There is currently a high demand for trauma/CCM trained surgeons. Down sides are liability, heavy call, patients who put themselves in their predicament.
Of the routes to doing critical care, the Pulm/CCM route is probably the most well rounded primarily because of the internal medicine background. Pulmonary cross training gives you bronchoscopy privileges (a primary billing procedure), Pulm consult privileges and outpatient exposure (if you want it). Plus the vent management training is the most progressive. I would definitely give a nod to the trauma/CCM guys too. I personally am a bit more a thinker than doer, liking the diagnostic challenges over the tactile challenges of trauma( 90% appy, perirectal abcesses). However, for any CCM, you have to have a high comfort level with and apptitude for both.
As for getting out of ambulatory medicine...accreditation requirements mandate outpatient training. Its not my favorite thing either, but you do need to get a sense for what happens to patients after they leave the hospital (and a hospitalists care). If you want CCM heavy training, look for programs where the IM residents do most of the procedures, and do the maximum allowed time in the ICU (6 months I believe).