I wildly disagree with the premise that the principle difference between european style socialism and the socialism practiced in china or NK or the USSR is whether the state or private ownership has the steering wheel. The difference is how dispersed and shared the power structure is between groups with differing ideas. Concentration of power inevitably leads to corruption and further concentration of power and unfettered private ownership is an incredibly efficient way for power to concentrate. Capitalism is a very powerful tool to create an oligarchy and if private ownership is allowed it will at least WANT to create an oligarchy given enough time. However, a one party system also WANTS to create an oligarchy, even if the one party ostensibly represents the people. The modern socialist movement contains many, many people who have little to no interest or belief in seeing pure communism happen.
We are going to have to agree to disagree on the modern common definitions of things then. If socialism means only be definition a transitionary stage to communism then there is no meaning in people saying they are a socialist vs a communist, but clearly many people identify as socialist but not communist.