Remaster != Remake != Reboot
Remaster= Pick an old game and change the native resolution and framerate.Models/textures/shaders may be improved(not always though).
Good examples: Wind Waker HD,The last of us R,Master chief collection,Devil may cry trilogy,Metal gear Solid collection,Zone of the enders.
Remake: A totally new version made from sketch.It's not an old game's update,It's a totally new game that retell the old game's story.
Good Examples: Resident evil Remake,Abyss Odyssey Remake.
Reboot: Similar to Remake,it's a totally new game made from sketch.The difference is that the reboot will not retell the old game's story,but have a new plot that will start a new universe different from the original but same characters.It's almost like a spin-off.
Good Examples: Tomb raider(2013),Silent hill Shattered memories.,DmC devil may cry.