So, to be clear, there is no way to save the normal save? There's no way to use a normal save from one version of the same emu to another?
If you have a regular save file from a game, you should be able to use it with different emulator versions.
The problem is that most NES games don't have save functionality, so no save files.
Also a save state is not the same as a save file. Save files are generated inside the game itself to keep your progress, when you hit the save button or similar.
A save state is created by the emulator in the emulator menu, this stores the exact state of the game. These often aren't compatible with other versions of the emulator, depending on what has changed between versions.