What the government does: we have heavy restrictions here based on the first amendment and for very good practical reasons.
What society does: which there are very few restrictions and rightly so.
What this means is if the government is suppressing speech, it's probably going to be unconstitutional and illegal. I think pretty much everyone agrees with this.
If society reacts negatively, then in my view it's not necessarily a suppression of speech. For example if bob has a radio show and comes up with an opinion that enough people dislike and bobs funding ends up getting pulled as a result, it's not suppression as bob does not have a right to his platform in the first place. Bobs radio show is nice but he has no right to it, so by it being taken away he has lost no rights. He is still just as able to express his opinion as his mouth still functions.
Now others view a negative societal reaction as a suppression of free speech. Honestly I am still trying to figure out why some would feel that way.