Short answers, pulled from the story.
The first officially licensed home console conversion of an arcade title occurred in 1980 with the release of Space Invaders on the Atari 2600. This event transformed the device from a niche curiosity into a household necessity and marked the birth of the modern video game remake.
Sega released the remake Pitfall II: Lost Caverns in 1985. This title combined the original Pitfall! and its sequel with new level layouts and colorful graphics to mark a departure from the strict fidelity of earlier ports.
The game Metroid was remade as Metroid Zero Mission in 2004. This version included the original game as a bonus feature after beating the game once.
The Skywind team reported having finished half of the remake environment by November 2014. This fan remake of Morrowind utilized the source code and assets of Skyrim with over 70 volunteers.
The demake Princess Rescue was released in 2013. This game was a demake of the NES title Super Mario Bros created to showcase the abilities of older generation systems.
A port relies heavily on existing work and assets from the source game, whereas a remake contains a great deal of remade assets. A port differs from a remake in that it still relies heavily on the original assets and engine of the source game.