A firmware is an IPSW file that contains everything needed to run the core operating system, iOS. Beta firmwares have also been released, but require an Apple Developer account to acquire. To check for updates, iTunes contacts itunes.apple.com.

Firmware List (by device)

Apple TV

Apple TV firmwares have two different version and build numbers, which can lead to confusion when referencing them. As such, the internal build number is the best way to refer to a specific firmware.

The "Marketing"/"Displayed" columns are what is reported on the Apple TV's "About" screen

The "Internal" column refers to the ProductVersion and ProductBuildVersion keys in the IPSW's BuildManifest.plist

Apple Watch

HomePod

iBridge

iPad

iPad Air

iPad Pro

iPad mini

iPhone

iPod touch