The “quit” button appears on every single app open in gnome. The “quit Skype” appears even on Windows, if you have set Skype to minimize to system tray when you close it, the “quit” button will minimize it to system tray, meaning the app is still open (you will see it in the top bar), while if you click on “quit Skype” it will log you off of Skype and close the app completely
It's up to the application developers. In case of Skype it's an old app. I don't belive it's in active development any longer but I'm not 100% certain. Anyway Skype for Linux has been neglected for years.