Don't you just love theories? I sure do. Let's analyse some of the theories that are most likely true. More will be added as time goes by.
The Destiny Gang theory
Look at that. Coincidence? I think not!
They are totally the same characters! If you want more proof besides their appearance only and the fact that they are a gang, they were both in a Jesse Moynihan/Tom Herpich episode. They even threw a basketball at Jake. That is just as insane as burning a town. Also, the Destiny Gang lives in the castle from The Creeps. That must be where the Pup Gang once lived, and the Ghost Lady is their mom! I am on to something.
The Fire Kingdom theory
I have a new theory that Flame Princess and the rest of the fire people were actually characters written by the Ice King. Remember when he said Flame Princess is "okay" even though she is under aged, but he was shown to not like under aged girls in Mortal Recoil? And remember how he wrote Fionna (and Cake) to love him? It seems like he loves his made up characters, despite their age for some reason. He must of gotten inspiration to write these characters not that long ago, perhaps only a few decades. Think about the first appearances of the Fire Kingdom - it seemed there were no buildings or even solid land to stand on yet. After seeing this land of nothing but fire and lava, he got straight to writing a story about his made up fire people and their kingdom. When he finally finished writing the story, he actually loved it so much that he decided to make it a reality, just like how he wanted the gender swaps to be real in Mystery Dungeon. However, the Ice King was successful in making the fire people real. Why else would he think the Ancient Magi of Life Giving would make the gender swapped characters come to life instead of the book, anyway? This may also explain why the Fire Count's face looked quite a bit like the Ice King's. He also got into stealing princesses because that is what the Ice King would do, and became evil after some time. Even the rest of the fire people were led down the wrong path after seeing how evil the Fire Count was.
Before the fan-fiction...
The Candy Kingdom was built on cursed grounds
Think about it. Despite the Candy Kingdom usually being a happy kingdom, there are numerous episodes where there is either a major problem or the fate of the kingdom was at stake. This can't be just because it is one of the main locations of the show, sometimes there is a major threat for no reason. Think about Hug Wolf and Little Dude, for example. Finn hugged a lot of the candy people in Hug Wolf, and Little Dude attacked the Candy Kingdom of all places he could have gone instead. Not only that, the guy who is deadset on capturing a princess and making her his wife likes Princess Bubblegum the most out of them all. Nice.
Ooo's population is critically low
Ever notice how weird it is how a lot of the characters in Ooo have tied pasts with eachother? Let me explain. Princess Bubblegum has had something to do with Flame Princess and a past relationship with Marceline. Finn and Jake just happen to have relationships with all those characters. As for Ice King, think about Mystery Dungeon. Out of ALL the people in the Land of Ooo, Ice King uses 4 reccuring characters to help him get to the Ancient Sleeping Magi of Life Giving. We didn't even know Ice King knew about all those characters (besides Beemo and Neptr), let alone what they are able to do! Now lets get to even more minor characters, there is actually a lot I can say, but to make it simple I will give only one example; the wizards. A lot of them like Bufo and the Forest Wizard have reappeared. These characters also appeared in Wizard Battle, and a lot of the wizards in that episode reappeared in Reign of Gunters. There was a small amount of never before seen wizards. Now think about the other times there have been reccuring characters. Wow, these episode connections that us fans love are beginning to look grim, now.