"Completely unrelated" is not quite true.
Stockfish current NNUE models are trained on LC0 training data.
LC0 is pretty much an open-source community replication of the ideas from AlphaZero.
I stand corrected. However, fundamentally, the idea of "tiny CPU-only neural network" combined with traditional alpha-beta search is substantially different from "big GPU network" combined with Monte Carlo Tree Search. And historically the NNUE came from a 2018 idea for shogi engines rather than from AlphaZero.