They inject something in the gums that removes sensitivity there so you feel nothing, and then have half your face frozen for 4h afterwards because it acts on the nearby nerves that control your facial muscles.

Having experienced both (frozen and not frozen), I can't tell what's better. The feeling when they're digging in the tooth without freezing isn't great but it's not painful either; the feeling when they put a needle in your gum to inject the product isn't great either but then you don't feel the procedure. I'd say it's different but equivalent in terms of discomfort.