Explain left and right to me (political terms)

[Yonadav]

In American terms:  

Left = Large government with a degree of wealth redistribution to social programs for retirement, healthcare, education, social safety nets, etc.
Right= Small government, free markets, minimal regulation, no redistribution of wealth.

These two visions of what government should be are not so compatible with each other.

The above is incorrect. It seems to be what americans are told but is basically flawed.

Left and right wing poilitics started with the French revolutionary parliament.

The people who supported the monarchy, centralising wealth and power sat to the right, the more they more extremes they were in those views the further right they sat.
The left were about wealth and power sharing and the more extreme they were in those views...you get the idea.

So lets look at right wing countries and left wing countries (not Stalinist communist as although it has some aspects of left wing the shows aspects of the right in its centralisation of power)

So left wing does not have to mean large government. Wealth distribution, well its more about building a fairer society that works better for all so more wealth equality but not redistribution which implies stealing money.
Socialist societies can have free markets why not. I would say that infrastructure and health care should not be part of the free market but where you buy your fish why not. So a mixed economy works best. In the UK we were better when more stuff was nationalised and the rot set in when Thatcher sold our services. Bus services are terrible now compared to when they were nationalised.

And the right wanting minimal regulation. true but dangerous, regulation is there for a purpose. Without regulation we would have more deaths and more shocks to the economy. It is unregulated markets that have led to all the major crashes.

I answered the question without loading my answer with my worldview. You read things into my answer that weren't there. Also, your notion that redistributing profit implies stealing money is a totally right wing.