Socialism is democratic/authoritarian government owning parts/the whole of the economy
Communism is a totalitarian government owning the whole economy
That's basically it, communism is simply the more extreme form of Communism and the only real difference is the extent by which the government interferes with the economy and private lives. In any case I can see a Communist Faction rising up easily. Most people forget that when communism rose in Russia there wasn't a very large amount of industrialization. As a matter of fact the primary reason Communism rose was due to a lack of industrialization in Russia in comparison to Germany which lead to staggering deaths in World War 1...Still most would argue without a industrialized middle/working class of some sort you can't have a communist rebellion, but that doesn't match up with China's revolution which was a peasent revolution.
This all said, the rise of a communist/socialist faction would have to be lead by an educated group of rebels who would cause revolts among the lower classes. It would best occur in a place like New Vegas. The residents are largely poor, the inequality is great, the Followers is already an empathic NGO that's produced a totalitarianist (Caeser). Honestly the slums of Vegas would be the best place for such a faction. Is it such a large gap of logic that a socailist member/s of the Follwers wouldn't try to improve the Followers mission through revolution or setting up of a government.