Just a quick answer, I would always use the "Exit" option when it will work. It is a much cleaner way to do it.
To "Kill" a process means exactly that, and therefore the program does not get to do any cleanup work it might want to do (like saving configuration, saving other files, etc...). Unless you know what the process is and that it does not have any "cleanup" to do, and even then, it's just cleaner to use "Exit."
There does not appear to be any difference between the two "Exit" options you mention, I would wager that the first is simply implicitly passing the zero value.