The Add to Cart button when you click adds Product to Cart and shows you the Cart display as it is selected under the Dashboard > Theme Settings > Shop > Shopping cart widget > Action after add to cart.
The Buy Now button redirects to the Checkout page or Cart page as you have selected under the Dashboard > Theme Settings > Single Product > Buy Now: https://snipboard.io/Xle7nA.jpg. There is no option to add a shopping cart popup after the buy now button.
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