> Communism: weak central government

This is not how it worked out in practice, no?

In terms of political theory, communism has always been (a somewhat utopian) theory that shares many ideas with anarchism. I like to think of communism as slightly more pragmatic, in that there's somewhat of an acknowledgement that there needs to be a agency that holds a monopoly on violence (a police force) - as a last resort to mitigate anti-social behaviour.

But if one reads eg Rosa Luxembourg, the lines are very much blurred between the two.

There's a tendency to spend time arguing that the various socialist states that where formed by communist parties were communist, because they were ran by organizations that labeled themselves (and indeed were) communist - I don't think such discussion is much more fruitful than discussing how the US attempted to "liberate" Vietnam, or institute "democracy" in Chile.