Connections to "It's my Life"

I read "It's my life" after reading this cause they're supposed to be connected, but other than the fact that meteors exist and the stuffed animal, are the two stories really connected? Like is there stuff in later chapters that ties them together, or do the KMKY characters make a cameo?
The two stories just seem to be happening in completely different worlds, with IML being a fantasy/mideval theme and KMKY being more of a post apocalyptic world (which is more depressing to live in) and the stories have really different tones.

One last thing: I thought maybe KMKY was like in the distant future of the IML story, but the stuffed animal appearing seems to say that IML occurred afterwards? So is it like really far in the future where people have started to make the world more livable?