Personally - and a lot of other anarchists do as well - I make a distinction between a government and a state. A government is any kind of collective organized decision-making, while a state is something more specific; an organization that enforces a hierarchy on a population without their consent by maintaining a monopoly on violence. In effect a state is an extreme concentration of power that both coerces and requires the participation of an entire population.

The anarchy that I envision isn't simply the abolition of the state, but its replacement with a non-hierarchical, horizontal form of government, which would also require - but not coerce - the participation of an entire population. There are many forms such a system can take, and there are some examples in today's world that show a glimpse of how such a system could look, like the autonomous region of north and east Syria (AANES or Rojava) which is practicing what they call Democratic Confederalism, or the Zapatistas in Chiapas Mexico with their federated local autonomous governments. There are also less totalizing organizations that practice horizontal decision-making and which could perform the various functions of government, and occasionally do in situations where the state is slow or fails to respond such as natural disasters or when a community is a victim of violence perpetrated by a state where no other state intervenes. Organized decentralized power is capable of countering, disbanding, and even preventing the concentration of centralized power.