That is also socialism. Communism is an imagining of what the world will look like after entering a state of post-scarcity. In fact, part of what is imagined in that is that we will become stateless. After all, absent of scarcity, what would you need a state for?

Now, it was once theorized that capitalists would artificially withhold entrance into post-scarcity and that the only way to achieve post-scarcity is, first, for the state to take over the means of production. This theory bred the Communist Party. States under rule of the Communist Party are often called Communist, but in that vein does not refer to capital ownership, but rather the party in power.