Correct but the government doesn't need to own the means of production; it only needs the power to control the means of production, which can be accomplished by enacting and enforcing regulations.
Yes I guess “controlling” the means can be thought of as socialism.
The reason I ask is because its a term used ad libitum and wonder if it is always correct to do so.
For instance a strong social safety net by itself would not be considered socialism(IMHO), but can be a characteristic of it.