Yes, Walmart has their own 'Walmart Radio' service. I'm guessing it's off some satellite feed? They play a lot of recent pop music but also play some '70s and '80s stuff.
Back when I worked at Wal-Mart (Christmas rush, 1987), they had Christmas muzak playing, all of it instrumental. Of course, since I was there all day at the time, I noticed a lot of repetition that the average customer probably would not have noticed.
But the best part is that now, stores like Wal-Mart typically do not use that loudspeaker pager system anymore. If employees need to speak to each other, they usually use their own personal pagers, cell-phones, walkie talkies, whatever. It was somewhat annoying, from the customer's point of view, to hear employees constantly paging each other over the loudspeaker. Technology has improved on that.
Sonic has their own network as well that plays a mix of music from the 50's to more current in rock, pop, country, and R&B.
We were just at Sonic last night. Sonic has their own "radio station" complete with djs, even taking requests. But last night when we were there, they had the volume turned significantly down, to the point that I almost could not hear it. We wanted to eat outside, but you know how it is with fickle middle/west TN weather. A little cool, so we ate in the car. As for Sonic radio taking requests, I don't know how, or even if, they could get to a request before the customer had to leave. As you said, quite a variety there. I don't know if it is even possible to listen to Sonic radio anywhere else, or if it is more of a closed-circuit, satellite feed.