It's possible that "censorship" denotatively means suppression of any speech (including the parade of horribles -- viagra spam, stolen IDs, abuse content, etc.) and connotatively means suppression of speech with at least some political valence. Or alternatively that it's denotatively ambiguous and has multiple connotations.
A case that sort of rubs up against this in the U.S. -- I use an American example because in Canada s.1 circumscribes all legal rights, including freedom of expression, so it would be academic whether this raised speech concerns or not -- is Morse v. Frederick.
In this case, a student, Frederick, raised a banner that read "Bong Hits 4 Jesus" in front of some television cameras. The behaviour occurred off school grounds but nearby, and during an event that students were allowed to leave school early to attend. The school suspended Frederick because his banner promoted drug use.
A lot of the ruling relied on parsing what category of speech this banner was. One argument is that it was essentially dadaist, absurdist speech (Frederick's claim. Another argument is that it was promoting criminal behaviour (the school principal's claim; Roberts, Scalia, Kennedy, Thomas, and Alito in the opinion). Another argument is that it was political speech, aimed at contesting a public policy (Stevens, Souter, Ginsberg in dissent; Alito and Kennedy in concurrence)
Although there were other issues in the case, namely to do with how speech is regulated within schools and whether this constituted a school event, one of the undercurrents is that constitutional protections for political speech seem to be more crucial to many of the justices than constitutional protections for gibberish speech.
So I don't think it's crazy to suggest, at a minimum, that there exists a well-support denotative use of "censorship" that specifically refers to speech with political characteristics, rather than all speech. Through that lens, copyright enforcement could either be censorship (to the extent that the enforcement is designed or has the effect of prohibiting the dissemination of political speech or prohibits commentary on a public policy) or not (to the extent the content being restricted is fundamentally apolitical). And this is true even if there are other denotations that consider stopping any speech to be censorship.