Are we supposed to update emulators from Emudeck only or we can update them also from inside the emulator itself?

I think the title is pretty clear. I ask this because when I update them from Emudeck, it says everything has been updated, then I open the emulator alone and it says there is an update available and I can download it from the emulator website. It happened to me with Duckstation and RetroArch.

Thank you in advance!