Capitalism - the government has little to no control over businesses
Socialism - the government has some control over businesses
Communism - the government has total or almost all control of businesses
"Socialized medicine" means when the government has control over healthcare in a country, meaning they have more strict laws concerning health insurance, doctors, and hospitals. This would stop doctor bills from getting too high, prevent people from not getting insurance, etc.
So it would be a good thing, right?
A lot of people think it would, including me, but the problem is that it would make taxes a lot higher. It can also make things harder if you are a doctor, because you could lose a lot of freedoms like deciding where you work. Some people think that if socialized medicine existed in the US, the government would force doctors to move to cities where they would be needed the most. But that may not necessarily be true.
In the strict Marxian sense capitalism is an economic system where the means of production are all privately owned and communism is an economic system where the means of production are all communally or publicly owned. Socialism was seen as an intermediate form where the private and public sector shares responsibility of the means of production.
Socialized medicine refers to health care administered by the government. We currently have a hybrid system. In general the private sector picks up the profitable business and the government picks up the unprofitable. In health care profits are privatized while liabilities are socialized.
Because cold war propaganda was so successful "socialized: is generally used as a pejorative term today. Americans tend to think that social- anything is evil and a slippery slope to totalitarian communism. Since no pure form of capitalism or communism exists all real systems could be considered socialist though.