The Desperate "Internet Censorship" Argument Against Copyright

During the protests against the Stop Online Piracy Act (SOPA), critics of the legislation portrayed its effects as "censorship" — full stop.

Lots of consumers are used to getting their content for free and would like to keep it that way. Giant tech companies are happy to avoid the pains of regulation and reduced profits that would come with rules-of-the-road that treat creators with more dignity. It's much easier and more effective to say they believe in "free expression" or are "against censorship" than to admit that they prefer artists to have little negotiating power and undervalued work.

Representatives from Google or the EFF, Reddit, etc are so quick to lump in the attempt to protect artists rights with the political censorship of China or Iran. Yet in Iran, newspapers are shut down for explicitly political reasons, not because of copyright infringement. I heard this story on NPR last weekend about a new law in China that forbids the "spreading of rumors" about the government, and bloggers are actually being arrested. Is this "censorship" the same as, say, making it more difficult for consumers to download unlicensed music and movies for free?