On the contrary, both in anarchist and marxist philosophy communism is defined as a society without State and social classes. While anarchists believe (and practice!) in dismantling the established social order here and now by systematically questioning power structures, marxist-leninists promoted the idea that building a "dictatorship of the proletariat" was a necessary step for a revolution to seize the repression means of the bourgeois State to make sure to go towards communism. This disagreement is what led to the fork of the 1st Internationale in the late 19th century.

As history has shown, reestablishing the old forms of power (centralized State, political police, prisons, work) for the sake of the revolution didn't help to achieve any communism ever (USSR was profoundly anti-communist beyond the appearances: the secret police fought against all self-organized communes like Cronstadt or the peasant soviets of Ukraine). That's why anarchists to this day refer to marxism-leninism (what capitalists call "communism") as State-capitalism: it has the same structures and power balance than capitalism, with the difference that power is held not by the bourgeoisie but by a so-called avant-garde. But for the common people, the situation is very similar, as the promised Stateless/classless society is nowhere to be seen.

Marx eventually clarified that he thought the “dictatorship of the proletariat” would not be a dictatorship, but instead rather radical democracy. With the benefit of hindsight, we can say that the anarchists’ criticism of Marx and his dictatorship of the proletariat were spot on, and that such structures rapidly became authoritarian and self serving.

Not really, Anarcho-Communism, while not Marxist, is communist insofar as it is one of the remaining strains of "Idealistic Communism" as Marx and Engels would call the various worker's movements from before Marx' Scientific Materialism.

Kropotkin described himself as an anarchist communist in the 1890’s. There is a lot of historical meaning in the combination of those terms.

Communism != Marxism.

In principle i agree, yet there is a distinction to make. There are anti-authoritarian marxists who argue that by the end of his life Marx himself had become critical of his own theories (eg. dictatorship of the proletariat).

But yes, we'll agree that the most widely-known brand of marxism is in fact the very opposite of communism (as defined by a Stateless/classless society).