This is not correct in my view. It doesn’t end at the Economic position. In the end it’s about not having the freedom of self determination. Means of production, property ownership, or otherwise. Socialism doesn’t end with the economic model, it can’t. It’s everything. Just as the WEF says today “you’ll own nothing and be happier”.
I think Winston Churchill said it best when he described it this way, “Socialism is the philosophy of failure, the creed of ignorance, and the gospel of envy.”
Trying to sub-factionalize Socialism seems like a canard to a bigger POV IMO.
Economic Freedom and Political/Personal Freedom are inextricably intertwined.
You cannot have one without the other. Which is why Socialism is Tyranny.
There is no way around it.