As a marketing person I get a kick how people mangle semantics, especially when talking about health care reform. So here are some simple definitions and examples where this is being used in the U.S. today:
Public Option: In essence a government entity set ups a competitive insurance carrier. After being setup, the taxpayers are paid back and the entity runs on its own. Both New Mexico and Utah (there may be more) have already done this years ago for workers compensation. The state legislatures set these companies up to drive down the cost through competition.
Single Payer: In this case, the government acts as the insurance carrier, collects premiums and uses private business to deliver the health care. Medicare is an example of this.
Socialized Medicine: Here the government runs everything. They collect the money, build the hospitals and clinics and hire the doctors. The Veterans Administration is an example of this.
As you can see, we have all three examples running currently. So when we discuss health care reform, let's understand what the words mean.