Backpropagation is the special case of reverse-mode automatic differentiation applied to a network's evaluation function composed with a scalar loss

The relationship between backpropagation and reverse-mode automatic differentiation is not analogy but instantiation, stated directly in the field's canonical survey (Baydin, Pearlmutter, Radul & Siskind, JMLR 2018): "The resulting algorithm is essentially equivalent to transforming the network evaluation function composed with the objective function under reverse mode AD, which, as we shall see, actually generalizes the backpropagation idea." And at the definition of the reverse mode itself: "AD in the reverse accumulation mode corresponds to a generalized backpropagation algorithm, in that it propagates derivatives backward from a given output."

The direction matters. Backpropagation is the narrower, neural-network- specific name; reverse-mode AD is the general method, applicable to arbitrary programs (branching, loops, recursion) via the chain rule over elementary operations. This one-way relationship is why priority questions about "backpropagation" resolve into questions about the reverse mode — the structure claim-linnainmaa-reverse-mode-single-pass describes for rounding-error sensitivities is the same structure gradient descent uses for weights, because both are the same algorithm applied to different composite functions. See backpropagation-gap and claim-reverse-mode-multiple-independent-discovery.