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Liminal Being is the general trope here- characters split between states or natures like Schrodinger's Cat, whether that be philosophically or literally. It sounds like this series is playing quite a bit with various forms of the trope and its subtropes via Reality Retcon. Also might be worth adding as an example of the most extreme end of Temporal Mutability.
The boy would be a Paradox Person, in that they exist in an impossible state of being both sick and well; the girl who went on the trip might also qualify as an example depending on what repercussions her paradox has.
There's a good chance Schrödinger's Butterfly is in play as well, if the characters or those around them wonder if they're going crazy.
See Ripple Effect Indicator for any strangeness that comes about because of all this messing with reality, and Ripple-Proof Memory for those who notice what's going on.
Edited by Scorpion451
That's great help, thanks!
In the anime Houkago no Pleiades, different possibilites exist at the same time due to alien shards.
(I was thinking this trope should have something to do with Schrödinger's Cat, but it doesn't seem to fit exactly.)
Example: Two girls both thought the other had left school, but it turns out they have been going to the same class, sitting by the same desk in the same chair. When they can finally see each other again, so can the rest of the class, who disagree on which of the girls used to sit there.
A boy has magical powers, while at the same time he is still sleeping in a hospital bed.
When the boy starts living a normal life, he starts going to school. Which would require him being enrolled, having a home with parents, etc. All of this existed as a possibility the whole time, and now he has switched to that possibility. Only the magical girls remember that he used to be different.
A girl travels away from Earth for several months. When she returns, she comes back to the day when she left. There was a chance that she would come back months later, and also a chance that she would come back on that day - the possibilities existed simultaneously.