[rplacd]

If you don't mind a parenthetical point, I'd argue that Marx's specific analyses and the precise names stuck to them are too limiting at this point - or at least I'm convinced you've conflated two properties that someone pointed out a while ago would make debate considerably more productive (by virtue, I suppose, of making the "heterodox" double-qualifier idelogies suddenly more motivated) when separated - the degree to which ownership and control of the means of production are centralized; and the precise ownership described in the terms of some separate dichotomy. Your point would prescribe for the first - but "socialism" as a name I'd claim has accreted and been recast to the extent that some synthetic history in which the limited-liability company is replaced with the cooperative would be called "market socialist" by last-generation Soviet nomenklatura, and yet "social-democratic and cooperativist" by the Co-operative Party that by agreement constitutes a curiously significant amount of British Labour (and hence the use of a name.) That's neither to argue, though, that the two are a mile and a half away: you're right to say that it did once imply both, and that in past contexts (or that's my impression of Western European economic reform post-World War II) it was overbearing as a trend no matter how the actual distribution of control could be construed.

(Edited for spelling correction, the contextualization at the end, and the note about how overt signs of association affect self-appropriation of names...)