Are extreme ends of the political spectrum the same?

Ever since I took a history course on the NSDAP (The Nazi Party) and a couple Modern British History courses, I've had an theory in my head that's never really gone away.

That theory is this:  Both extreme ends of the political spectrum essentially lead to the same thing; a state with seemingly unlimited authority over its people and the country's economy.  A state that will stop at nothing to continue to preserve itself at the expense of its people.

It all depends on how you define what the left is and what the right is and perhaps even a little bit of history of that country to help guide you on finding that.

So, what is the left?  In the United States and most of the western world, the left involves equality and increasing liberties to all, and economically it involves state intervention in the economy at all levels.  The left  sees the state as a way to help its people by making life easier for them by some kind of a welfare system, a national health service, and a pension system; all done to enhance the quality of life.

What is the right?  While the left is generally seen as a progression, the right is seen as preservation of society in that country.  Economically the right is against government intervention in the economy, and less government programs, as the government is seen as a barrier or force that can infringe on the people's personal liberties.

So what are the extreme ends of these?

Let's start with the right.  The way I see it, the extreme right can be two things:

1.  Complete Anarchy
2.  An authoritarian state with strict laws to preserve the country and a strong military police to enforce the laws and detain those that do not conform or meet the state's requirements.

And now the extreme left.  I see it as one thing:

An authoritarian state which controls the economy in all ways, high taxes, and sole provider for the people.  Whereas the far right has strict laws to preserve the status quo, the extreme left has strict laws to enforce equality and political correctness, but like the extreme right, the extreme left would have a military police to enforce these laws.

An example of the far right would be the Third Reich in Germany from 1933 to 1945, ruled by the NSDAP and Adolf Hitler.

An example of the far left would be the USSR in Russia, the Soviet State ruled by one party, the Communist Party and lead by many dictators, among them was Joseph Stalin.

It's in my opinion that there's very little difference in either of these, the only differences being how these countries got to this end.  Both lead to a tyrannical, authoritative state that says they're interested in serving the people, but in actuality, enslaving them to maintain the power of the state.  There can only be one voice in these places; both the USSR and NSDAP Germany banned any opposition to their parties.

Let me know your thoughts.  I intend to continue a topic of what is America?  Is it right, left, or maybe the middle?  What is the middle and can there be a equilibrium on the political spectrum.  And at some point I'd like to tackle the two party system here in the US.  Are they really all that different?