The difference is, theoretically at least, that in a socialist system, property is owned by the community at large. In strictly totalitarian systems (pure dictatorships), all property is owned and controlled by the government, period.
BTW, Hitler intended to establish at true totalitarian form of government. He only paid lip service to the desires of the people.
No, in a socialist system property is privately owned, and can be bought and sold, but regardless of who owns it, it must be managed for the purposes of the state.
In a communist system it is communally owned, cannot be bought or sold, and is managed by the state.