I watch CR and think: this is a lot like my home game. The same beats and rhythms, people playing their characters, lots of laughter mixed in with a bit of drama. The DM does their best job of creating an exciting campaign and does a variety of voices and mannerisms (well, I do, many do not and that's okay). A lot less shopping/exposition most of the time but that's something that varies from table to table.
Are they more "focused"? I don't know but maybe my games are unusual because we tend to stay in character just about as much on the show. Maybe it's because we get a bunch of chit-chat out of the way when we're first together and take a lunch break set aside to just hang out. Having structured breaks in game time means there's not a lot of out of game stuff at our table, about the same amount as I see on CR. Our actual play time is probably a bit longer than most CR episodes.
Are they aware that this will be watched? Obviously. I just don't see how that makes it "fundamentally different than a home game".
But this has now devolved into:
Me: "CR reminds me of my home game."
Others: "It's a performance for an audience, it's not at all the same."
Me: "Well, when I DM I am performing, to a certain degree when I'm not DMing I'm still acting the role of a PC".
Others: "It's not the same. They get paid"
Me: "Right, but how does that matter? We speak in person at our table. I do voices. Maybe not as eloquent..."
Others: "It's not the same at all"
Me: "Huh? How?"
Others: "Because it's a performance for an audience"
Put on spin cycle. I'm done having that argument, we might as well be cutting and pasting at this moment.