I'm going to copy my response from Wright's thread:
Enhanced port -- a nearly identical game experience with glossier graphics and maybe improved frame rate. Nice for people who never had a chance to play the original, but, ultimately, superfluous. Examples: God of War Collection, Banjo-Kazooie
Remaster/Partial remake -- an expansion of the original title with redone graphics and sound, and some notable gameplay changes. Examples: The Wind Waker HD, The Secret of Monkey Island: Special Edition
Full Remake -- a new interpretation of an old game with new audio-visual assets and altered gameplay. A complete reimagining of the original source material. Examples: GoldenEye 007, Bionic Commando Rearmed