When Stockfish evaluates a position, it explores moves to a greater depth (a greater number of plays ahead), with its guesses and the value of the final board arrangements it can get to estimated using a relatively simple heuristic. AlphaZero evaluates the different potential moves using the neural network, which guides the search with a very complex heuristic that implicitly incorporates a tremendous amount of depth from prior games that have been incorporated into the model. Similar to the way an image recognition model takes in a whole image and says "this is an image of a goat," AlphaZero takes in a whole board and says "this is a winning board."