Propagation is completely wave-like. It is unitary and time reversible, without loss of information. There is no particle there, and no 'there' there, as the propagation is non-local. Waves have complex amplitudes. Interference happens because that's what waves do. Propagation is described by the Schrodinger/Dirac equation.
Interaction is completely particle-like. The interaction is non-unitary and time-irreversible. The interaction may also be known as detection or measurement.
The wave only contributes the probability of the interaction happening, which is described by the Born Rule. Amplitudes are complex, so squaring them with the Born Rule can give negative probabilities, which is why the double-slit experiment gives many fringes.
The interaction is local, because it creates the 'there'. Positions and distances are created by the interaction as a specific spacetime event. Hence the aphorism spooky distance at an action, meaning that (inter)action is fundamental, and distance is a strange thing created as a byproduct.
There are conservation laws that balance some incoming and outgoing properties, scattering laws that determine how the interaction happens for various forces, and some constraints between the knowable values of commuting pairs of observable state (particle properties) that are revealed (entangled) by the interaction. These constraints are also known as Heisenberg's Uncertainty Principle, but are really just direct and obvious mathematical properties of wave packets, as described by Fourier Analysis.
After the interaction, there will be propagation of new waves for the outgoing particles (meaning a bundles of state). The interaction results in an entanglement (correlation of future possible interactions) between these distinct outgoing waves.
That's it.