"Game Saves" depend on the core being used, because some consoles attach pseudo devices as memory cards, while others like NES emulate the storage cart in the game cartridge. All of these use files on the emulator filesystem to store the actual saves, but use the game code to save data as the game is designed to do, and will show as saves in the game. Each core will have its own docs on how this works.

"Save States" are a point in time dump of the game state that sort of replays data where it was saved from. Like pausing music or a video. these are also dumped to files, but loaded differently, and will not show as saves in game menus.