How is the distinction hard to understand? Socialism is a system characterised by social ownership of the means of production, as opposed to capitalism, which is characterised by private ownership of the means of production. Both are ideologies.
You could have compared to Soviet or East Germany directly if you wanted to make a point about totalitarian regimes.
Also, I'm pretty sure Germans don't consider socialism to be an authoritarian ideology. Maybe you're confusing it with national socialism (nationalsozialismus => nazism).