As usual, definitions are highly overloaded and mean lots of things to different people. I believe you're referring to "true communism" which even Marx saw as something of a mystic nirvana over the rainbow that wasn't likely to arrive anytime soon. I wouldn't really call Marx a small-government type; he certainly believed some form of government, in the sense of institutionalized force against class enemies to enforce the perfect society, was required.
http://en.wikipedia.org/wiki/Paris_Commune#Retrospect has some reasonable details on it; while obviously Marx was a huge fan of the Commune in general, his complaint with it was that they were too merciful to capitalists and spent too much time worrying about democracy rather than seizing power, etc. When people say "communist states" in 1970 or whatever they almost assuredly mean the Marxist-Lenninist or Maoist definition, in both of which there's still a dictatorship of the protelariat where the Communist Party runs everything in an incredibly powerful single-party state to prepare the way for the happy governmentless society.... which is very, very, very far off. I'm not sure the far-off Promised Land of a stateless society is enough to qualify communism as a "small-government movement at its core" when every actual communist state hasn't really gone that way.
Anyway, Western European leftist parties usually identified as "socialist", got elected, and actually held power, so I'm inclined to let their definition be "socialism" as they're the notable ones who practiced it. Stein would probably be at home in the various French socialist parties so I'm fine with calling her a socialist (and also acknowledging that by the American definition of liberal, she is super-liberal, which is not the same as the European or Australian definition of liberal, etc.).