To me there is a clear distinction between both types. Sometimes it gets blurry if they use different techniques from both sides. There is also the term “Port”, which is less of a “Remaster”. So its even more blurry, even when I try to formally describe it. Here is my definition:

• Remaster: Basically taking the same code and base and “recompile” it for a new version. Graphics are usually not remade, programming code is the same (but with touch ups off course). Rather it has higher resolution output from original graphics, like higher res textures compiled from original resources, adding functionality to make the game compatible with modern hardware and features like HDR and gamepads in example.
• Remake: Making a new game from scratch, programming it again (off course they can take over old stuff), with new graphics to approximate the same game. Sometimes they even manage to make the game look and feel the same, where people think its a Remaster. But in fact it is programmed from scratch and has no common source in anymore, it is just faithfully recreated.

Off course this is just one mans definition. And both terms are used somewhere in between, and people don’t share my opinion. Therefore I never know if the game is a Remaster or Remake actually.