Path Integral vs. Wave Equation?

This will definitely reveal my ignorance, but from what I know the path integral of a quantum particle is something like a weighted sum of all the possible paths the particle can take. Since a quantum particle’s wavefunction obeys a (complex) wave equation, can we think of non-quantum waves as being weighted sums of paths of individual particles?

I am confident that there is something that I am very wrong about in this question, but please enlighten me.