Communism, the classless, fully collectivized system of production and distribution, has not existed yet. It is a post-socialist mode of production. Socialism is a mode of production where public ownership is the principal aspect of the economy, and is the transition between capitalism and communism. Socialist countries exist that are run by communist parties, and some of these states do have billionaires as they have not fully collectivized production and distribution.
I think you're misunderstanding the transition between capitalism and communism. Where did you get your understanding of what socialism and communism look like from?