Well, there seems to be lots of confusion and I'm not sure, too. Maybe because many games are ports with remade elements.
A port is bringing the game (based on the same code) to another platform. The resolution can differ and the textures are identical to the original release or worse (handheld ports for example).
If you use the term "remaster" in analogy to movies and music it should mean that new textures are created from the uncompressed original assets at a higher resolution than the original release. Like a movie gets a new digital transfer of the original film. But the term is also stupid because video games don't even have a mastering in the same way that Blu-rays or CDs have it...
Remake: (all?) assets newly created and not based on the old code.
