I don't think either term fully fits, the game sits somewhere in between. I'd say it's more accurately either a well done remaster or a cheap remake.
All they really did was upgrade the texture quality, add a much better lighting engine, repeatedly smash the bloom button and render it in 1080p. There are also some slight model and artistic changes, but for the most part the in-game geometry is identical to the original. It's somewhat a testament to how well the original has aged that these changes allow WWHD to look almost as good as many new WiiU titles.
Were it simply a texture/resolution upgrade (as seen below) we would all agree it was a remaster. The improved lighting and artistic changes do make it stand out as a bigger improvement than many remasters, but i wouldn't say by enough to justify the term "remake".
WW HD textures:
WWHD WiiU:
