Official Firmware
"Official Firmware" is any firmware that is installed through the "System Update" option in the PlayStation 3's XrossMediaBar. The PlayStation 3 game console can only have one official Sony firmware installed on it at one time. When you select the "System Update" option from the "Settings" section of the system's XMB and follow through with the update, the previous firmware is removed from the system and the new firmware is installed.
Unofficial Firmware
Unofficial firmware is any "jailbreak firmware" or any firmware not installed through the "System Update" option in the XMB. The PlayStation 3 game console can only have one type of unofficial firmware installed at a time. As soon as you install a different type of unofficial firmware, the old firmware is deleted. If you install official firmware over an unofficial firmware, the unofficial firmware is deleted and if you install an unofficial firmware over an official firmware, the official firmware is deleted.
Two Hard Drives
Some users believe that they may install two separate firmwares on two separate hard drives and swap them out of the PS3 system whenever they want to use a different firmware. This is not the case. The system's firmware is not located on the removable and replaceable hard drive, but is instead stored on the system's flash memory. The hard drive, therefore, has nothing to do with the console's firmware.
OtherOS
When the PlayStation 3 console launched, it came with a featured titled "OtherOS." While this feature did not let you install a separate PS3 firmware on the system, it did let you run a second operating system on the system. With the release of the PlayStation Slim console and the 3.21 firmware update, Sony removed this feature from the PlayStation 3 system.