Anarchists don't want a fully publicly owned and planned global republic, Marxists do. Anarchists want networks of decentralized communes, Marxists do not.

The "state" for Marxists is the oppressive elements of society that make up class distinctions, such as private property rights and the current police structure, whereas for Anarchists its usually seen as a form of hierarchy entrenched with violence.

Chiefly, a decentralized network of communed does not get rid of class, but entrenches petite bourgeois class structures where each commune owns only what is within its commune, whereas Marxists want to abolish class by making all property equally owned by all in a highly developed and complex economy.