These could not be any more opposite.
Commumism believe in strong, central rule.
Anarchism believes in no central rulers, but rules and governance provided by the marketplace.
Now there ARE many communist and leftist type groups that CALL themselves anarchist, which is why much confusion often arises, and why libertarian anarchists will often describe themselves as anarcho-capitalist to distinguish between those that call for communist-style "anarchism".
*Advancing the Ideas of Liberty Daily*