To the contrary, it's the only consistent application of either. If socialism is when the the means of production are controlled by the workers, then is it real

To the contrary, it's the only consistent application of either. If socialism is when the the means of production are controlled by the workers, then is it really socialism if a government is the one controlling those means, merely on "behalf" of the workers? Likewise, there is inevitably a hierarchy between those that control the means of production and those that don't, creating rulers in any system that grants exclusive ownership of those means to individuals. Thus you cannot have anarchy ("an-": without "archy": rulers) without socialism. Most anarchist movements in history have been socialist: the CNT in Spain, the Anarchists in the US who played a major role in the labor struggle around the turn of the 20th century, the Black Army in revolutionary Russia.