Ok let me broaden my definition to include your example:
libertarianism: a society where your wealth belongs to you and cannot be taken by force
socialism: a society in which wealth is forcibly transferred from one person to another for any purpose.
The net result is the same. Libertarianism is the philosophy that you own your body and the proceeds of your labor. Socialism is the philosophy that wealth should be taken from some people and given to other people. These two philosophies are completely incompatible.
In a pure libertarian economy there would be no taxes, as all services would be paid for privately. For example, if you wanted a road, you would have to pay someone to make it and arrange for a toll system. There would be no government that states it is in everyone's best interest for there to be a road and therefore we will tax everyone on the assumption that everyone gets equal use out of the road.
Now in reality government is useful for situations like roads where so many people get the same benefit that it mostly evens out on average. Here is where socialism comes in to play: socialism is when the government takes money from one person and gives it to another directly. This is distinct from the example with the road, because the road could be used by anyone and is therefore a "public good". Another example of a public good would be street lights or postal service. Socialism is the transfer of wealth not for public goods, but for goods that the government says is entitled. Taking my money to pay for your doctor visit is socialism, since I can not benefit from your doctor visit no matter how much your healthiness contributes to society as a whole.