There is one set of observations, and many many models to describe them: Schrödinger equation formulation, matrix mechanics (Heisenberg, Born, and Jordan), path integral formulation (Feynman), phase space formulation, density matrix formulation, QFT or second quantization, variational formulation, pilot wave theory aka de Broglie-Bohm theory, Hamilton-Jacobi formulation, PT-symmetric quantum mechanics, Dirac equation formulation (well, not really independent, just for spin 1/2 particles).
They all give the same results, and are therefore mathematically equivalent, but different models tend to be associated with different interpretations:
Schrödinger Equation : Copenhagen, Bohmian Mechanics, Many-Worlds
Matrix Mechanics : Copenhagen
Path Integral : Many-Worlds, Stochastic
Density Matrix: Ensemble, Decoherence-based
Second Quantization : Many-Worlds
Pilot Wave Theory : Bohmian Mechanics
Consistent Histories : Decoherence-based
Relational QM : Relational Interpretation
Stochastic Models : Stochastic Interpretations, GRW (Ghirardi–Rimini–Weber) Collapse
There is one set of observations, and many many models to describe them: Schrödinger equation formulation, matrix mechanics (Heisenberg, Born, and Jordan), path integral formulation (Feynman), phase space formulation, density matrix formulation, QFT or second quantization, variational formulation, pilot wave theory aka de Broglie-Bohm theory, Hamilton-Jacobi formulation, PT-symmetric quantum mechanics, Dirac equation formulation (well, not really independent, just for spin 1/2 particles).
They all give the same results, and are therefore mathematically equivalent, but different models tend to be associated with different interpretations: