(Or, if you'd prefer, reboots or re-imaginings -- me, I'm not sure those terms have much use outside of marketing designed to avoid the stigma of remakes).
I think reboot has a purpose when it's talking about getting a franchise
to reset rather than an individual film. I mean Abrams' Star Trek
and Batman Begins
and Casino Royale
are not remakes of previous films, but they are clearing the detrius of their preceding films and getting back to basics. The stories may be derived or partly derived from other sources but none of them are straight up remakes of an earlier picture.
While van Sant's Psycho
or the Coen Brothers Ladykillers
are straight remakes of previous tales, retelling the same story with the same characters.
I don't think they're mutually exclusive terms, obviously - nuBSG can be fairly called both a reboot and a remake and one could argue the same for Rise of the Planet of the Apes
(a quasi-remake of Conquest of the Planet of the Apes
as much as it was also cleaning the slate of the Apes
franchise) and so on.
Re-imagining though remains to me the pretentious term thrown around for Tim Burton's Planet of the Apes