Marxists are communists, for whom the end goal is a stateless, moneyless, society. What do you think stateless means?

Good question. Marx specifically referred to the State as the mechanisms within government by which one class asserts its power, not the entire government. Engels elaborates on this, and explains the "whithering away" of the state:

"The proletariat seizes from state power and turns the means of production into state property to begin with. But thereby it abolishes itself as the proletariat, abolishes all class distinctions and class antagonisms, and abolishes also the state as state. Society thus far, operating amid class antagonisms, needed the state, that is, an organization of the particular exploiting class, for the maintenance of its external conditions of production, and, therefore, especially, for the purpose of forcibly keeping the exploited class in the conditions of oppression determined by the given mode of production (slavery, serfdom or bondage, wage-labor). The state was the official representative of society as a whole, its concentration in a visible corporation. But it was this only insofar as it was the state of that class which itself represented, for its own time, society as a whole: in ancient times, the state of slave-owning citizens; in the Middle Ages, of the feudal nobility; in our own time, of the bourgeoisie. When at last it becomes the real representative of the whole of society, it renders itself unnecessary. As soon as there is no longer any social class to be held in subjection, as soon as class rule, and the individual struggle for existence based upon the present anarchy in production, with the collisions and excesses arising from this struggle, are removed, nothing more remains to be held in subjection — nothing necessitating a special coercive force, a state. The first act by which the state really comes forward as the representative of the whole of society — the taking possession of the means of production in the name of society — is also its last independent act as a state. State interference in social relations becomes, in one domain after another, superfluous, and then dies down of itself. The government of persons is replaced by the administration of things, and by the conduct of processes of production. The state is not ’abolished’. It withers away. This gives the measure of the value of the phrase ’a free people’s state’, both as to its justifiable use for a long time from an agitational point of view, and as to its ultimate scientific insufficiency; and also of the so-called anarchists’ demand that the state be abolished overnight."

This is not the Anarchist definition of the State, best described as a monopoly on violence. For Anarchists, elected councils are examples of vertical hierarchy that ought be opposed, as compared to Marxists who see it as a necessary tool for administration. This is the transformation from "the government of people" to the "administration of things," ie government and councils and committees exist to fulfill managerial roles, while Anarchists seek full horizontalism and avoid managerial roles as they believe them to lead to corruption and coercion.

Think Star Trek vs. The Disposessed.

And as the process. Which is what separates it from other communists.

Yes, I am familiar with Means/Ends Unity. I may disagree with the importance of it, but I am not here to promote infighting or sectarianism, I am here to explain Marxism.

Building them up through grassroots movements. They don't happen by taking control of the government and creating "elected committees" who then "plan production", which is what the comic talks about doing (even adding a picture of Lenin), and which the other user - and you by extension - defended.

Yes, you build up Anarchism, a network of horizontal structures, from the bottom up. You build up Marxism by building dual power via councils, unions, and other democratic structures that can replace the Capialist state. These are separate concepts with similar but distinct goals.