A non-technical ELI5 explanation.
A barcode only stores data horizontally, while a QR code stores data both horizontally and vertically.
Take a barcode that has 5cm width and 5cm height, it can only store 5cm of data, even though the height of the barcode is also 5cm.
A QR code that is 5cm width and 5cm height, however, can store 5cm * 5cm = 25cm² worth of data.
It may not be technically correct, but it’s good enough for a 5 years old.
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