Okay well then you're arguing that there are no necessary conditions for classifying anything.
Nope. I'm just pointing out that you're employing a classically fallacious argument form and no amount of attempting to semantically parse it into validity is going to ever work as a result.
Socialism is fundamentally a critique of the power structures intrinsic in capital relations (which are typically expressed in terms of profit, interest, and rent). The base moral claim of socialism is that people ought not have power wielded over them simply because they're trying to survive.
The way you have defined socialism, literally anything that proclaims to be a critique of capitalist relations can fall under its rubrik. The second sentence, which proclaims the moral intents of socialism, is simply irrelevant. I couldn't care less what the moral intentions of socialism proclaims to be.
This definition, the first sentence of the quoted text, is vacuous and without meaning or substance. By this definition, State Capitalism is absolutely consistent with the overarching rubrik of socialism, in that it attempts to critique the power structures of capital relations by ensuring that there is a facilitator which mediates between the typical mechanisms of the means of production and distribution which we call the state.
Let's go with the definition of socialism I get just typing "socialism define" into google for example:
so·cial·ism
ˈsōSHəˌlizəm/Submit
noun
a political and economic theory of social organization that advocates that the means of production, distribution, and exchange should be owned or regulated by the community as a whole.
synonyms: leftism, welfarism; More
policy or practice based on the political and economic theory of socialism.
synonyms: leftism, welfarism; More
(in Marxist theory) a transitional social state between the overthrow of capitalism and the realization of communism.
By all of these definitions, as well, State Capitalism is a subset of socialism, in that it is a political and economic theory of social organizatoins in which the means of production, distribution and exchange are owned or regulated by the community as a whole through the mechanism of the state. It is also considered a possible transitional state between the overthrow of capitalism and the realization of communism.
Your argument is simply vacuous on its face, Mik.
Sorry bro.
Anyway, like I said, we've reached an impasse where we cannot proceed further. You're not going to get me to cede that your no true scotsman isn't the dictionary definition of the form of that argument structure, and thus fundamentally flawed at its core, and I'm not going to convince you that the distinction you are perceiving is ultimately meaningless in the same way you judged the theological implications of Jesus' execution date and time and the division between Shi'a and Sunni Islam to be ultimately inconsequential.
So since neither can budge on these points, it is pointless to continue any further.