Unlocked means not tied one network, like AT&T or TMobile. You can obtain an unlock code for a GSM phone in various ways, TMobile will actually provide that code is you have had the phone long enough.

Factory unlocked is just that, the phone was never locked to one carrier when it was sold.

Debranded is removing all special screens, menus, and software that ties a phone to a particular company. This may also mean not having a phone company name on the exterior of the phone as well.

You may lose some specific network functionality with such a phone. If all you do is make calls and the occasional text, it won’t matter. MMS, Internet, wifi, that sort of of thing, may not work properly.