So having socialist features in a capitalist economy is not unusual. The forms of economic systems are feudalism, slavery, socialism, communism and traditional selling and trading in goods and services. Like when the US combined slavery and capitalism to sell and trade human beings. As feudalism, which frequently involved slavery, broke down, capitalism was rampant in cities and villages while kings still ruled over everything, combining feudalism and capitalism.
The ownership of the means of production by a democratic or representative state is normally understood to be communism or state socialism.
Though Karl Marx does not make a very dramatic difference between the 2. He always saw communism as the ultimate goal with socialism as just a transitory phase but I think he was wrong there.
So, the state doesn't have to own the means of production for it to be socialism. The means of production just has to be collectively owned and controlled.
It is difficult to break apart the type of government from the type of economic system. During Marx's time they were considered the same thing or very closely intertwined. You can have socialist organizational styles and you can have socialist states, or you can have neither, or both or just one. That's the problem when you put labels on human behavior, it is always imperfect.
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