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AlphaZero uses Monte Carlo Tree Search not MinMax. So it does use a neural network for the search. Modern Stockfish is the one that moved to having a neural network for position evaluation while keeping MinMax with AlphaBeta and heuristics for the search.

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Nitpick: MCTS is a heuristic search algorithm as well (just like minimax) that doesn't necessarily need a neural network to operate and the MCTS algorithm existed way before AlphaZero, coming from Reinforcement Learning literature. Deepmind's innovation was to replace two of the 4 classic steps of MCTS (selection step and simulation step) with neural network-based policy and evaluation network.

That's a good nitpick. In recent computer chess discussions MCTS is usually shorthand for the search that was novel with AlphaZero and then copied by LeelaChessZero. But you're absolutely right, MCTS doesn't even need to imply a neural network.

Oops! You are right, I got alphazero and stockfish mixed up.

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