Super Mario Advance 4: "You can only load this game once" message
The message is the difference between a regular save game, and a feature that's commonly known as quicksave.
Most games have specific points where you can save the game, right? Either a time, like right after a boss, or a place with actual save points, or only on the world map, or something like that. Starting around GBA times, somebody realized it should be more convenient. Possibly in the rush to port all the old nostalgia games somebody realized what a pain is was to actually lose progress if you had to turn the thing off right away.
Quicksave started showing up as a way to "pause" through a shut down, even though the game restricted where you can save. It was a save anywhere anytime option, but worked almost exactly like a game pause in every respect. Quicksaving the game also exited the game so you couldn't keep playing, and reloading the game with quicksave put you right back where you were and wiped the quicksave. It never actually acted like a save file at all.
I'd have to load up my copy of Advance 4 to be sure, but that sounds exactly like every other quicksave feature I've run into.