I think the visions of people floating up into the sky are somewhat fanciful and are the result of people reading too literally into a translation. The actual Rapture is just whichever people qualify suddenly dropping dead on the spot as their souls are whisked away. Some probably get put on life support machines but never wake up again.
This is the biblically accurate version. In heaven the body has no more purpose than the clothes people wear, so the bodies should just drop dead empty of souls.
However, a more terrifying interpretation could be that the bodies have no reason to just drop dead just because the soul is gone, instead, they would continue functioning as P-Zombies. This could mean the rapture already happened and we're just not aware of it. If you are not a P-Zombie, you weren't raptured. This could be a premise for a pretty cool story.
This is not the biblical teaching about the body. The hope emphasized in the Bible is for the resurrection of the body. This is why Jesus is resurrected bodily, and not as some kind of ghost. If the body was some kind of superfluous thing like clothes, this would make no sense. This is also why the Nicene Creed says “I look for the resurrection of the dead, and the life of the World to Come.” The World to Come likewise is a renewed version of this world, where Heaven and Earth are united, in the same way that the body and soul are. This idea of the soul shedding the body is Platonic, not Christian.
As for the rapture itself, it is considered to be nonsense by virtually all biblical scholars, both secular and religious, but how it became such a widespread belief among Americans is probably for another website.
The Rapture is more of a pop culture thing than a widespread belief among Americans, but there is one notable exception: Evangelicals. For some reason Evangelicals latch on to some of the weirder parts of Christianity.
