Earlier quoted context omitted.
It is distinctly different because the government can fine me or imprison me if I violate their legal proscriptions. I can't opt out of those restrictions. If Google blocks my content or otherwise refuses to host my content I have lots of other options. Your assertion that Google is a monopoly is this regard is not accurate.
If the government censors you, you have other choices as well. You can publish your content in locations outside your government's jurisdiction. So basically your "imprisonment" qualification on the definition of censorship is completely arbitrary and does not stand up to critical scrutiny.
If Google takes down my video, and I publish it elsewhere, there's no real risk of anything. Maybe I'll lose my Google account if the video was particularly heinous, but that's about as far as it goes.
The imprisonment qualification is a very real difference.