Well, one way is just by distinguishing the terms “anarchistic socialism” and “state socialism.” Francis Tandy (a follower of Tucker) used the term “voluntary socialism.” Today, Kevin Carson likes to use the term “free market anti-capitalism”.

If more than two or three words are needed, you can explain that, even though most people today use “socialism” to refer only to state socialists, anarchistic socialism has been around as part of the socialist movement longer than Marxism and Social Democracy have, and that anarchistic socialism is based on the idea that workers should own the means of production, either individually or as part of voluntary associations, rather than the government owning the means of production, as state socialists suggest. You might also point interested parties to Benjamin Tucker’s essay, “State Socialism and Anarchism: How Far They Agree and Wherein They Differ,” which explicitly mentions Proudhon and his ideas, and is, I think, one of the finest discussions of the distinction ever put to paper.

You write: “PLEASE NOTE THAT PROUDHON WAS BY NO MEANS A SOCIALIST, AT LEAST NOT BY THE MODERN DEFINITION OF THE TERM, …”

Well. Proudhon certainly was a Socialist by his own definition of the term, and by the definition of the term that was widely in use at the time amongst other people who called themselves Socialists. In the General Idea, he flatly states that Socialism is “the new name for the Revolution,” and also that “But an idea cannot perish. It is born again, always from its contradictory. Let Rousseau triumph: his glory of a moment will be but the more detested. While waiting for the theoretical and practical deduction of the Contractual Idea, complete trial of the principle of authority will serve for the education of Humanity. From the fulness of this political evolution, we finally arise the opposite hypothesis: Government, exhausting itself, will give birth to Socialism as its historic sequel.”

If many people who use the word “Socialism” today think that it implies something incompatible with Proudhon’s views (e.g. government expropriation of the means of production, or central economic planning by the state), that hardly settles the question of whether or not Proudhon should be called a Socialist. Those people may be using the word incorrectly or confusedly. Or they may be using it as part of an ideological package-deal, which should be combated rather than pandered to. I for one see no reason why the views of Karl Marx, Eduard Bernstein, V.I. Lenin, or whoever you like have a better claim to the word “Socialism” than the views of Proudhon, or other anarchistic socialists, such as Josiah Warren, Benjamin Tucker, Victor Yarros, et al. Proudhon came to both the term and the movement years before Karl Marx ever did, and there is an old and continuing tradition of anarchistic socialism that rejects, root and branch, the Marxist disaster of State monopoly and State planning.

Many people today misunderstand what the word “anarchist” means; they think that an anarchist is someone who advocates riot and social disorder. Nothing could be further from the views that Proudhon was referring to when he called himself an “anarchist.” Does that mean we should go around saying, “Proudhon was by no means an Anarchist, at least not in the modern definition of the term”? No, of course not. What we should do is correct the misconceptions that people have about the meaning of the term “Anarchism.”