For a while, Russia moved away from the Soviet way of doing things. It gave up satellite states and even had a few peaceful changes of power. But Putin's an old KGB guy, and is trying to reinstate the Soviet Union, in fact if not in name. He's created one-party rule, under the effective dictatorial control of a single person, and he's been using military aggression to try to rebuild Russia's control over Eastern Europe.
That said, there are differences, as well. For example, most of the Soviet leaders were remarkably effective, helping to take Russia from being a weak and backwards nation of serfs to being a relatively prosperous superpower (and the first nation to send someone to space) in just a couple generations. They turned it into one of the world's great powers, and an inspiration to countless other nations that tried to follow them into communism. Putin, by comparison, is a total incompetent, who took a nation with vast oil wealth and turned into to an economic backwater, political pariah, and laughing-stock military, almost totally devoid of allies.