That's an interesting question about how power works in communism. I think that kind of system is supposed to be driven by the class consciousness of workers. It's a collectivist state, fueled by Marxist or Leninist rhetoric about the glories to come from the empowerment of humble workers, at the expense of the do-nothing, spoiled aristocrats. This was a hard-headed, materialistic, and even scientistic philosophy. The point was that workers would save the day and generate social progress, by being uncorrupted and purified by honest labour. They'd own the fruits of their labour so there would be no need for fraud to rationalize alienating profits.

But communism in that sense fails if only because of the law of oligarchy. Workers don't unite perfectly in that sense because class divisions are needed to manage any complex society.

Greed is indeed different from money since we can be greedy about obtaining different things. But money is a medium of exchange, not of power. Money can give us power and everything else that can be exchanged for the units of the currency.

You'd have to be more specific about what you mean by "power." I think of power over other people, and of human power over nature. Does money itself exacerbate greed for those kinds of power? Of course, money is a tool that can be used in different ways. But my point was that money facilitates economic inequality, and thus power over other people, because money can be accumulated whereas votes, for instance, are equally distributed.