There is a difference between "social" and "socialism". The social welfare state was invented by Bismarck
in order to fight socialism.
Thus calling it "socialist" is a pretty gross error. Indeed the foreign minster of Denmark had to plead with uninformed Americans to please stop calling his nation "socialist" when it is a social democracy - this was back when Bernie was running as a democratic socialist and his schtick to try to normalize socialism was by saying Denmark had it which lead to this mess of misinformation.
The idea of social democracy is that you have social welfare programs. That is, you tax private industry and give the money to people for things like pensions (which is exactly what Bismarck did, and this basic model has not changed since it was developed in 19th C Germany).
Socialism is the idea that private ownership of the means of production be banned (thus you cannot own your own business). In communism, all private property is banned (thus you don't even own your clothes, or car, or apartment).
Obviously the utopia of banning all private property was impractical, but seizing factories was more practical. Thus even those nations that were controlled by communist parties officially declared that they had not reached communism, they were in the state of socialism, and were working towards, or "building" communism. This led to many jokes in the Eastern Bloc about when the building of communism would be completed and how could it be done with all the shortages, etc. That is why all the communist nations called themselves socialist. Now you know the difference between communism and socialism.
What about socialism versus democracy. Here the problem is the enormous amount of totalitarian government control needed to organize production based on political concerns rather than concerns of price -- e.g. market concerns. Even if you are just a painter, you need paint. How do you get the paint? You have to requisition it based on some political justification. Now the government needs to plan how much paint is produced each year. Then you need to plan how many paint buckets and paint brushes. It goes on and on. There were mathematicians working full time on these linear programming problems in the soviet union, just trying to figure out how to plan their economy. Imagine all the inputs you need, imagine writing them down, and requisitioning them, as part of a big five year plan.
This requires a vast array of secret police and government micromanagement and that is what makes socialism not free. Whereas the genius of Bismarck is that he understood that workers just wanted pensions, and did not care so much about political organization of the process of production. So it's a lot easier to tax private enterprise -- something that was done even in ancient Mesopotamia -- rather than trying to control the process of production. Thus social welfare states are more "free" than socialist states, and no socialist state can be free, it must be micromanaged by the Party. Nevertheless they all called themselves Democratic. E.g. the Democratic Republic of Germany.
Thus we have these two types of economies, the social welfare state and the "democratic" socialist state, but they are not gradations on the same scale, they are two rival approaches to the problem of providing a basic safety net for the people.
In one approach you do it by taxing and giving people money who then go out and buy what they need on the open market, and in the other by political administration of production and then political distribution of production to those groups you believe "deserve" the output the most.
It is not two ends of the same scale.