Compatibility Testing
Compatibility testing verifies that software works correctly across the different environments it might run in — browsers, operating systems, devices, screen sizes, and versions of dependent software. It exists because "works on my machine" is rarely proof it works everywhere a real user might be.
Compatibility testing typically runs against a defined support matrix — the specific combinations of browser, OS, and device version a team has committed to supporting — rather than every theoretically possible combination, which is infinite and not worth chasing completely.
Cross-browser testing and mobile compatibility testing are the two most common flavors, usually run on cloud device farms (BrowserStack, Sauce Labs, LambdaTest) rather than a physical lab of real devices, since maintaining that lab in-house doesn't scale past a handful of configurations.