I prefer this way of looking at it:
Basically it separates the authoritarians from the libertarians on the economic left, and it separates the left-wing environmentalists from the right-wing environmentalists on the social scale.
Socialists on these boards and others seem to agree on the economics bit - about taking things into public ownership. However, that seems to be as far as it goes and the left has never dealt with the "social" side of things. Party discipline vs open debate.
People when discussing "what socialism means" need to make clear whether they are libertarian or authoritiarian in their disposition.