You are loosely interpreting the word "suppression".
Moderation is more akin to taking back an already provided microphone than it is to "suppression". The baseline for a person's ability to speak does not include someone else's forum.
A common example of censorship is with music on the radio: Musicians record a song which contains the word "fuck", which radio hosts would like to play in its entirety, but the hosts are regulated by a third party (government) to remove the word "fuck" from the track while broadcasting the song in the public radio spectrum. In this case, a third party (government) is constraining the radio host's ability to play a song on their own station. Because the radio host would normally be able to put whatever content they want on their station without assistance from a third party, this is censorship.
On the other hand, if a radio host decides to have a guest on their program, and chooses to end the broadcast before that guest is finished speaking, it is not censorship. The host is not suppressing the guest's inherent ability to speak, but instead are simply removing the microphone and audience they provided in the first place.
The irony is that the latter case is extremely common practice for many right-wing radio hosts who are equating moderation with censorship; yet these hosts do not claim they are practicing censorship themselves (they are not), even when rudely talking over guests or focusing on their own talking points.
> one is just the more palatable way to express the other.
If you would have bothered to read my comment, you would have learned that there is an explicit difference in meaning beyond a core idea.
> It's just as much the case on many left wing broadcast media. Don't conflate "left wing" with "openness".
I didn't mention "left wing" at all, nor did I imply that "left wing media" was any better than "right-wing media". Don't conflate criticism of "right-wing media" with blind faith in "left-wing media". My point was that it is "right-wing media" that are wrongly equating moderation with censorship here.