Some physicians are in private practice. This means that they see patients in an office or clinic and usually follow their patients when they are in the hospital. They bill for their services or receive capitated payments from an HMO (often a blend of the two).
Some physicians are full time faculty at a medical school, they are academic physicians. Many see patients in out-patient (office) and in-patient (hospital) settings, teach medical students and/or residents and often do some research as well.
Some private practice physicians are "voluntary faculty" on a medical school which means that they support themselves by caring for patients but they do some teaching at the bedside or provide small group training in things like physical diagnosis skills in exchange for the prestige of a "teaching appointment". This usually goes along with admitting privledges at a "teaching hospital".
Some (very few) physicians are employed by hospitals (or are technically "private practice" and bill for their services) but work only in the hospital setting, taking care of patients in the hospital so that the "private practice doc" can stay in the office seeing patients rather than running back & forth between the office & the hospital. This is called a "hospitalist" and it is a growing area but one that is controversial with clinicians and patients.
Health policy people may or may not be docs. They are interested in the rules, regulations, laws, etc that go into the way health care is delivered. What will happen if the State goes to an HMO-model for the care of Medicaid patients? That's the sort of issue that health policy wonks deal with.
Health administration is the actual business end of running a hospital or other service provider. They are thinking about "market share", "market penetration", competition, recruiting and staffing, salaries and benefits (for allied health professionals and other workers), what it will take to computerize this and that, the effect that St. Elsewhere" new cardiac unit is going to have on admissions to their own unit. Many who are docs have an MBA or an MPH. Some people in health administration have a degree in public health (some schools offer a concentration in hospital administration) or business but aren't docs.
Public health involves the community as the "patient". Some public health folks study outbreaks of disease and risk factors for disease. These are epidemiologists. Others are concerned with health administration issues around providing a safety net of services to those who are otherwise without care. Some are involved in health policy decisions, either helping to craft laws and regulations or in advocacy for population groups who would benefit from changes in public policy (e.g. prohibitions of smoking in restaurants as it impacts on the health of restaurant workers). Some people in public health are administrators of small or large groups of employees who do the work a public health department such as restaurant & septic system inspections, regulation of day care facilities and barbers, keeping of vital statistics (information on birth & death certificates and analysis of that data).
