Now the physical meaning of these 2 different rules are debated. In the standard (Copenhagen) interpretation of QM, it doesn't make sense to talk about the properties of particles until you measure them, so neither the wave function nor the Born rule can be given a physical meaning.
In the MWI interpretation, all results of the Schrodinger equation exist in different worlds, so there is no collapse, the detector just finds out "in which world you live".
In superdeterministic theories, the Schrodinger equation is just an approximation of a currently unkown fully deterministic theory of motion.
In pilot-wave theory, the Schrodinger equation describes an actual wave that particles generate themselves (the motion of the wave and the motion of the particle influence each other); entangled particles are just particles that live on the same wave. There is no collapse here, but the wave from each particle exists in the whole universe and can change non-locally.
Can you say more about that? What are the alternatives to being a physical phenomenon?