You're mostly dead wrong. Classical liberalism is a lot closer to what we call libertarian today, and was the source of laissez faire and other aspects of liberal philosophy now associated with conservative politics. For reference, the founding fathers were flaming liberals. Had they been conservatives, they'd have been royalists.

Yes, the Nazis called themselves socialists. They weren't. They were more like fascists, although that word was coined by Il Duce specifically to describe what was going on in Italy at the time, and Benito was quite clear in defining himself as both right wing and the polar opposite of Marx. So, big shock, Hitler misrepresented himself. I know some greedy murderous bastards who have professed devout belief in a man who taught people to eschew wealth, turn the other cheek and love their enemy. Guess what? They're misrepresenting themselves, too. There is a huge difference between what someone claims to be and what they, in fact, are.

One principle difference between communism and fascism lies in the diffusion of authority. A fascist government is extremely centralized, basically a corporate state. A communist society executed according to Marx would have no government at all save the "dictatorship of the proletariat." Absolute diffusion of authority. Marxism is the economic equivalent of direct democracy, where the people themselves, as a group, own the means of production among themselves. The trouble with Marx is the same problem with direct democracy; namely, that it becomes logistically impossible to execute on any scale larger than, say, a city-state. That's where communism is in danger of becomming fascism, when someone steps up to "organize things," (and in fairness that happens pretty much right off the bat) but you have to understand that it stops being communism at that point, no matter what Stalin says. You can accuse Marx of coming up with a system that was utterly unrealistic and prohibitively difficult to pull off, but you can't call communism and fascism the same thing. At most, you can echo the line by Dirty Harry about going so far in one direction that you meet the freaks coming at you from another direction. That's some deep wisdom there; to a moderate, anyway.

Social democracy, which is what most of Europe does these days, is basically the same kind of market state that we have, with competition and entrepreneurship with only certain industries defined as critical and placed beyond the reach of market forces. And we ourselves walk this path to an extent with public schools, fire departments, police and so on. Our freeway system is a result of a socialist program, which was so successful that we take it for granted today. You pay higher taxes in Europe, but then so would we if we decided to not finance so many things with deficit spending.

By the way, there is no natural connection between conservative and right wing, or liberal and left wing. Conservative values are merely traditional values, or at least what is thought of as traditional, according to the society in question. A liberal is simply a progressive who swims against these constraints, but still this is contingent on where you are and how people roll there. Right and left wing are a little bit more set in stone, thanks to where people sat in the French National Assembly following the revolution in 1789.

Half of America's problem is that it simply doesn't know what these words mean, and it clouds any attempt at political discourse. We tend to lump everyone we happen to not agree with in huge catch-all baskets and arbitrarily stick them with a bad sounding label like "leftist." The GWOT gives us even more examples of this principle in action, as we tend to lump groups with vastly different religious ideologies, political motivations, levels of numeric strength and degrees of political legitimacy in the same "terrorist" bucket based solely on one tactic that they may employ when faced with a much stronger adversary. It's a sloppy way to run an empire, if you ask me.

:-)