marxism

I'd say the common definition of a state is an entity with a monopoly on violence within a particular geographic area, and this is not something Marxists generally disagree with as it's a surprisingly materialist understanding of power. The function of a state according to Marxism is to use this monopoly to enforce class relations, which is part of the reason that Leninists view the state as a tool for class struggle, as a socialist/communist state can enforce pro-worker class relations and eventually end the class distinction (this is why Lenin theorized the state would "wither away", because if there are no difference in classes there's nothing to enforce).

So to address your confusion between Marxists and Anarchists, both ultimately do not want the state because it is a coercive tool to enforce specifc class relations, but the Marxists view it as a neutral tool whereas anarchists view it as inherently oppressive and cannot be used positively. Some anarchists view that, rather than classes, the ultimate source of oppression is the state and that is why it must be abolished which is a break from the Marxist view as it either ignores class conflict or folds it into critique of the state.