Thanks for clarifying what seems to be a pernicious confusion about the meaning of these terms. Sadly I think many people would have to abandon their pet prejudices in order to speak of these terms with the appropriate precision and historical nuance you've provided.
One of the most neglected aspects of Marx is that he thought that capitalism was an inevitable, natural development of industry. He also thought that it was a system full of contradictions and deduced that those contradictions would eventually cause it to transform into another system, communism. Communism was already a wildly popular movement by the time Marx started writing. What he set out to do was explain why there was a conflict in which one side was called capitalism and another was called communism and how that conflict would play out.
Marx's biggest failing was that he did not consider a third possibility: fascism. Such a populist movement was inconceivable to Marx, the epitome of an enlightenment thinker.
I think your analysis is correct; regardless of one's personal sympathies it's important to get the terms correct when discussing these issues. I think the image of what Socialism is has been corrupted based on misinterpretations of its meaning, especially in my judgement in the US. The fact that some people are downvoting my comment perhaps shows how ingrained biases are, and I am very far from perfect having only read the major Socialist authors, so it would be nice to be corrected if anyone has such a correction - though I doubt I will be; HN and Reddit are similar in that "drive-by" downvotes are common.
I remarked elsewhere that the art of dialectic was at some point lost; in Plato's dialogues the method was used to free the other person's soul from contradictions by advancing questioning of their assumptions and models. On mass platforms this cannot arise, as one's reputability (which should be irrelevant) comes into question via the usage of downvotes, and further the downvotes do not advance the dialectic, they aim to put a halt to it. It were as if there were, in the time of Socrates, a man sitting at the table during a diologue who did not engage but merely remarked "That's wrong!" or "I disapprove!".
Pretty much any political discourse has to start with definitions because these terms have become so encumbered with propaganda and double meanings as to be almost meaningless otherwise.
