The notion of “state” differs wildly across people, so that probably adds to the confusion.

The core concept is that ownership of a thing belongs to the people of the thing. This is where it clashes with feudalism and capitalism, where ownership of e.g. a farm is not held by the farm workers.

The organizational unit is “group of people cooperating”, or a “commune”. This can be small, like a hippie farm, or it can be big - a traditional state.

A democratic state can be communist if it forbids private ownership of common resources. I.e. your house is your house and your car is your car but some rich fuck can’t decide to build a fence around the local hiking trail.

An authoritarian state may technically be communist if it is strongly democratic. That is theoretical. The ones currently claiming communism are dictatorships.