“QR code” can mean a couple different things. There is a connection between these two, though that’s not at all obvious.
What almost everyone thinks of as a QR code is a quick response code, a grid of black and white squares that encode some data. For example, the QR code below contains my contact info.
There’s also something in algebraic coding theory called a QR code, a quadratic residue code. These are error-correcting codes that are related to whether numbers are squares or not modulo a prime.
The connection between quick response codes and quadratic residue codes is that both involve error-correcting codes. However, quick response codes use Reed-Solomon codes for error correction, not quadratic residue codes. Reed-Solomon codes are robust to long sequences of error, which is important for quick response codes since, for example, a row of the image might be cut off. It would be cute if QR (quick response) codes used QR (quadratic residue) codes, but alas they don’t.