These two atmospheres are forever classified as "Beer Run Emergencies" and "Smart phone Menace". These do not require the presence of actual beer or smart phones; it is merely the short hand for what poses the most immediate danger to the atmosphere you have generated.
"Beer Run Emergencies"
This type of table atmosphere can involve "Beer and Pretzel" gaming, but it doesn't have to. Really serious games can have this too, especially strategy board games or games like poker and chess. The important point is that it doesn't slow down the game if someone needs to leave the game to go do something else. This could be a beer run, or to get the walk-in pizza special, or even just to go outside and have a smoke. This doesn't mean one has to be able to leave for a long period of time (though it may), but people should be able to walk up and leave for 5 minutes, come back, sit back down and not have stopped other people from playing. Some games are awesome for this, high level D&D with a few wizards would often allow other players a few minutes to have a smoke or talk to their spouse on the cell phone (in the other room) before they have to go again. Most of the good examples I can think of this type of games are board games however, so I won't bore you with examples.
"Smart Phone Menace"
This type of table atmosphere is not "really deep plot driven story games" (though they can fall under it), it also involves silly games, casual games, all sorts of games. The main feature is that someone always has something to do, even if it isn't their turn. People are never sitting around bored waiting for their next turn, they are always eagerly paying attention. If they aren't paying attention however, this slows the game down for everyone else. This is great for groups where a few minutes of downtime leads them to boredom. I reference smart phones, but it could also apply to looking at other game books, building dice towers, etc. In these groups downtime is bad because once people zone out, when it gets back to their turn it takes an extra 10 minutes to fill them back in (after 2 minutes of "I just need to finish this email!"), which just accumulates as the problem spreads around the table until no one is really having much fun.
I make no secret that I designed Neoclassical Geek Revival to combat the smart phone menace. It fits how I like to both play and run games; I don't like sitting around doing nothing because I don't tend to multi-task. When I book time for gaming, I usually don't have other things to do on the side.
Other people have a perfectly good time with gaming as a secondary task, they are also listening to music, cooking on a barbeque, talking to other guests doing something else entirely in a different room, the game is just one part of their game night. When you are selecting a game for your group, or building a game to work on, be sure you know how you envision people playing it as they sit around the table. More than just mechanics, ask yourself what will the people be physically doing? Will they be laughing over drinks? Staring at their character sheet/battle grid/other players with furrowed brows looking for a solution? Chatting with each other about a solution? How do your mechanics make that easier or harder?