In his famous letter to Arnold Ruge, Marx says that “communism,” referring not to “some imagined, possible communism, but to communism as it actually exists in the teachings” of the living communists of his day, “is a dogmatic abstraction.”
Marx and Engels called their book the “communist” manifesto in a move to appeal to popular intellectual currents in the European working class movement circa 1848. Likewise with socialism, which is a more modern term referring to the realization of the potential of (bourgeois) society (i.e., “society” as such, considered as global humanity, as a solution to the 19th century “social problem” of mass unemployment, poverty, economic depression, dehumanizing industrial labor, etc.), as opposed to communism, which itself contains an idealization of the primitive human community, Marx did not invent the term; he was a critic of both socialism and communism, of the international workers’ movement then groping for such politics variously labelled, but from within these very movements, from the perspective of advancing their consciousness. He provided critique in the sense of clarifying the historical conditions of possibility along with their own potential for self-overcoming, insisting his work’s “task must be to latch onto these” already existing phenomena “as they are and not to oppose them with any ready-made system…”
“Nothing prevents us, therefore, from lining our criticism with a criticism of politics, from taking sides in politics, i.e., from entering into real struggles and identifying ourselves with them. This does not mean that we shall confront the world with new doctrinaire principles and proclaim: Here is the truth, on your knees before it! It means that we shall develop for the world new principles from the existing principles of the world. We shall not say: Abandon your struggles, they are mere folly; let us provide you with true campaign-slogans. Instead, we shall simply show the world why it is struggling, and consciousness of this is a thing it must acquire whether it wishes or not.
The reform of consciousness consists entirely in making the world aware of its own consciousness, in arousing it from its dream of itself, in explaining its own actions to it…
Our programme must be: the reform of consciousness not through dogmas but by analyzing mystical consciousness obscure to itself, whether it appear in religious or political form. It will then become plain that the world has long since dreamed of something of which it needs only to become conscious for it to possess it in reality. It will then become plain that our task is not to draw a sharp mental line between past and future, but to complete the thought of the past. Lastly, it will becomes plain that mankind will not begin any new work, but will consciously bring about the completion of its old work.”
That “thought of the past” and “old work” was the liberating transformation of the world into a global society based on the free exchange of labor, which in capitalism has now transformed into the form of the (given the immense wasted potential) most profound unfreedom humans have ever known. “Communism” is the name (particularly post-Revolutionary French) intellectuals, on the side of the workers’ struggle for the value of their labor, gave to the future society they theorized would transcend the situation which gave rise to those struggles.
“If we have no business with the construction of the future or with organizing it for all time, there can still be no doubt about the task confronting us at present: the ruthless criticism of the existing order, ruthless in that it will shrink neither from its own discoveries, nor from conflict with the powers that be.”
That’s a cursory stab at what “communism” means for Marx and Marxism, anyway.