is chrome and polished chrome the same
Yes, it's the same thing. Chrome is by default polished by which is meant bright and shiny. It does not have to be. There is brushed chrome, matte chrome, etc., but it is almost always identified by the adjective qualifier. There is such a thing as highly polished chrome, which is chrome that has in fact been carefully polished, sometimes called mirror-like chrome. Take a look at aRestoration Hardware chrome faucet for an example.