Neither the OR nor the AND descriptions are great as they give you just a partial (wrong) intuition of what the mathematical model says. Moreover, the mathemati

Neither the OR nor the AND descriptions are great as they give you just a partial (wrong) intuition of what the mathematical model says. Moreover, the mathematical model can always be wrong (although improbable in this case). But to address your comment: the OR description is a bit better than the AND one because the possiblities described by the wave function are excluding one another (when a good basis is chosen). However neither the OR nor the AND description actually mention the fact that the "probabilities" interfere (which is what the double slit experiment tests). That experiment disproves both of these simplified descriptions. Another reason I like the OR intuition better if I have to chose between these two wrong simplifications: if you do the double slit experiment with one photon at a time and repeat it multiple time then you do see only one photon at a time hit the screen (the OR intuition). But the image you get if you wait and average over many photons is indeed the interference pattern. TLDR: OR acts more like probabilistic but not interfering particles. AND acts more like waves. Both are wrong, but in different contexts one or the other might be a convenient simplification.