The progression is clear. At first, the internet was an uncensored free-for-all where anyone could publish anything and the search engines did their best to index it all.
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Eventually, national governments began requiring search engines to censor according to national law. So Google and others introduced country-specific versions where local censorship was contained in-country.
The internet has entered a new phase, where the dark side of information globalization becomes more apparent in our everyday activity
And then the worst fears of free speech advocates were realized. Governments began insisting that global internet resources censor content based on local, national norms, laws and court rulings.
The world before global censorship
The truth is that Google has long been censored globally based on the laws of one nation. That nation was the United States. For example, Google has been actively and globally censoring in accordance with the U.S. Digital Millennium Copyright Act for years.
There is no U.S.-specific version of Google. There's regular Google, which is subject to censorship according to U.S. law, and now there are nation-specific versions subject to the local laws of those countries. Still, U.S.-driven censorship has been minimal because of the First Amendment and a cultural norm of generally tolerating free-speech in the U.S.