There can be no such thing. Anarchists don’t just oppose the state, they oppose all hierarchies and authority. Capitalism is based on inequality and authority, with a tiny class of capitalists ruling over the rest of the population.
An anarcho-communist is a person who believes in anarcho-communism, a form of anarchism advocating the abolition of state and capitalism in favour of voluntary organizations through which people would satisfy their needs.
An anarcho-capitalist is a person who believes in anarcho-capitalism, the belief that advocates individual self-ownership.
All Communists are anarcho-communists, standing for a society with government or rulers, and no markets or wages either.
An anarchist communist supports a society with o government, no classes and no buying or selling. All Communists are also anarchists, though they may not use that label.