I categorize remasters as the following:
Remastered last gen games (Wii, PS3, 360)
Remastered fifth to sixth gen games (PS - PS2 Era)
Remastered third to fourth gen games (Nes - SNES era)
Remastered first to second gen games. (Atari era)
Generally, a remastered game from an older generation is less controversial and better received than those from more recent generations. But we already knew that
For remakes, I agree with OttoniBastos's definition. I'm not sure how to categorize those because I never played them before.