I've read the answers (and linked notes) to another question (Tree level QFT and classical fields/particles) and I understand them. They seem to explain how to organise a perturbative calculation of the solution to a classical non-linear ODE by drawing diagrams which look a bit like Feynman diagrams. But it is not clear to me how these diagrams correspond to actual Feynman diagrams. In QFT, when Feynman diagrams are used when doing path integrals (to calculate correlation functions etc.) but not to solve for the fields. What does the tree-level expansion of a correlation function mean and what is its classical interpretation?