I guess this set, called Santa's Crew, is meant to represent various holiday "characters" - Santa and an elf and so forth:
This second one is the only one with what looks like the "normal" Bonita bottle - as you can see, each one of these three sets has a different bottle shape. This one is called Jolly Nails, and it has glitters and metallics and what looks like a couple of plain old cremes. (The silver and gold metallics are the ones that interest me the most!)
Actually on reflection (I've now looked at the bottle pictures, but I decided this was the case before I even looked) I don't think this is the same bottle as the ones I have - which are Bonita Salon. Here is the Bonita website, where you can see that there are actually a number of lines, all with different bottles. But it doesn't particularly look like they used any of the regular bottles on any of these sets.
The third picture is terribly out-of-focus but since you can see the polishes so I'm including it anyway. This set is called Mani-More and it seems to be more on the glitter & shimmer end of things:
(I'm sort of wishing now that I had gotten names on these colors, but I didn't. I have no idea whether any of these are regular Bonita colors or what.)
The other set that I thought was interesting enough to take a picture of is from Cover Girl. I have several of these colors, and I think at least some of them are the colors that were released this time last year as a Catching Fire tie-in, in Glosstini size. They all have more or less the same glass-fleck-ish finish. Some of them were already core colors, I think, and at some point during the year this year the ones that weren't already core became core. They are some of my favorites, really, but since I already have (possibly) half of the six, it wouldn't be worth it for me to buy the set. I did look to see if the names matched, and they did, although I don't remember what they all were. The three I have with this finish are Seared Bronze, Pyro Pink, and Violet Flicker. (I may also have a black one, which I don't remember the name of offhand. But it doesn't seem to be included in this set in any case.)
(Here's All Lacquered Up's pictures of the collection, so you can get a better idea if you're interested. Going by what she says there, I think the black one I mention above must be Midnight Magic.)