Socialized medicine is a somewhat slippery term to define since people may perceive it in different ways. This is especially the case in the US where efforts to create some form of large scale government-involved health system have been underway for a long time. The push towards this system didn't just begin in the 1990s when then First Lady Hillary Clinton worked on creating a plan. Instead it goes back to President Theodore Roosevelt, who suggested public health insurance in the early 20th century.
By socialized medicine, some people mean that the government would pay for health care, often in exchange for higher taxation. People would not pay for most health care services as covered by the government. Such systems exist in places like Canada and the UK. There are options in both countries to carry other private insurance, and in Canada, most citizens pay extra for prescription drug coverage. Yet most costs for doctor’s visits or surgeries are fully covered.
The term “socialized” as is presently used, can be considered pejorative, especially for any who oppose US government involvement in health care delivery. It is used in place of socialism, and may be used to create fear or concern that government exerts too much control on people as is, and that allowing government to “control” health care would be taking the country in a socialist direction. When used in a negative sense, there tends to be glossing over of the fact that the US government has several “socialized medicine” programs. These include the Medicaid system and the State Children’s Health Information Program (SCHIP). To a degree, the health programs that cover the US military and Medicare are also socialized.
Those in favor of creating a government health system, even if it retains many private options, do not necessarily call systems proposed socialized medicine. They can refer to them as public health, universal health, single payer or public option. The idea of socialism, especially as evoking fear of the Cold War or sometimes communist states is given little credence. In fact some opponents of the term suggest "socialized" would have to become the adjective in front of many government systems that rely on taxpayers, and note few people refer to road systems as socialized roads, or to post offices as socialized mail.
What this really means when trying to define the system from a US perspective is that definition can very much depend on political orientation. It should be noted there’s a shift in this, as it was a Republican president who first proposed national health care. Today, it would be fair to state that most on the right are more opposed to what they deem socialized medicine, while most on the left support some form of government health care.