98% of the time people are talking about the former, and the only ones confused are the people assuming they're talking about the latter and linking the face-palm-worthy "showing them the door" XKCD.
I'd say damn near 100% of those 98% will still cite the constitution, sometimes even crying "1st amendment!" in lieu of "free speech," so I'd say your overall point is wrong. They are basically saying both at the same time, with intent, while still not understanding it.
What do you feel would be the good-faith way to respond to such people?
Surely it's not by sidetracking into pedantry about the law, which at the end of the day both they and you know that's not what they're really fired up about.
If the explanation is that they feel that other people have an obligation to listen to them, then I don't care.
My freedom of speech includes the freedom to reject other people's speech. If they can't tell the difference between a disagreement and suppression of speech, then that's their problem. The generous interpretation is that they don't fully understand the issue. The realistic explanation is that many people value their own freedom of speech over the freedom of others to the extent that they view disagreement with their views as an attack on their right to hold their views.
Essentially, "freedom for me but not for thee", and I don't rightly care about what enemies of freedom are "fired up" about.
But at the end of the day, much of what conservative "free speech" protests against big tech have been about has been that big tech drew a line on things like violence and hatred of protected classes, and conservatives don't like being told that their ideas, while legally allowed, are not welcome in polite company.
EDIT: I just realized you were not responding to me... oops!
My point (less snarkily this time) was that their definition (it's only an issue when the government limits your speech) is really quite narrow.
As long as there are a litany of people like you who are totally comfortable with a double standard like this, the only option for conservatives is to exercise power and forcefully shove the shoe on the other foot until you change your mind.
I hate that, but I don't really see another way we'll ever get a culture of free speech, because people like you are completely comfortable exercising power towards a culture of, ironically, "free speech for me but not for thee"
How is it obviously not true (genuine question)? I am not an American myself, but used the American definition as it's the simplest (it's very absolutist, as per my understanding). But what definitions exist where it is not defined in terms of how the government can treat you? I'm from Canada. We have concessions against hate speech, for example (maybe the US does too, though? I'm not sure). But "free speech" doesn't mean you are free criticism from fellow citizens or even businesses based on what you say.