I think there's a place for good remakes and remasters, especially for very old games, and games not originally released on many platforms. But the industry has come to abusing them just to churn out more.
Remake -> Take an old game and remake it from the ground up. Like different graphics, engine or even gameplay.
Re-release -> Simply release an older game again, possibly on another system, but don't do anything beyond perhaps the most basic of fixes to ensure compatibility.
Though I appreciate the reply, I was looking for the difference between a remaster and a remake specifically. I think both of them should mean the same thing essentially.