You kind of have it backwards though. Communism is considered the eventual result after socialism. The only reason government ever was involved in any of these systems is because that's how it's manipulated and plundered. None of these systems needs a government to operate but when the people start to realize it isn't working on a grand scale and want out, the government maintains its implementation for the purpose of control and abuse.
Except that socialism is specifically defined as government ownership and control of the means of production.
Communism is specifically defined as a stateless form of existence where the people hold the means of production in common as a collective.
Socialism must, by definition, be a government-run system.
My argument is that government is a necessary evil. No matter how hard we may try, government will always exist in some form. Thus, communism (like anarchy) is only possible for a very brief period of time. Thereby, communism leads to socialism, not the other way around.
.