What s the difference between an unlocked mobile phone and a factory unlocked mobile phone?

What is the difference between an unlocked cell phone and a factory unlocked cell phone? And what phone debranded?

Related posts:

1. What is the technical difference between a SmartPhone and a PDA?
2. HP iPaq 910 Windows Mobile Smartphone (Unlocked GSM)
3. How to Unlock Nokia Mobile Phone
4. BlackBerry 9700 Bold Unlocked Smartphone with 3 MP Camera, Bluetooth, 3G, Wi-Fi, and MicroSd Slot –International Version with no Warranty
5. BlackBerry 8700C Qwerty Unlocked SmartPhone –International Version With No Warranty