They're separate applications. Each has its own sandboxed space. You'll need to load the databases up to 14 (or download from 13, and then up to 14).
Yes. You have 2 versions of the files! There is no sharing between go... You can select one of the files in the FMGo13 base directory (from inside Go13) and press the 'go-out' - icon... a list of apps will appear that can open them, FMGo14 is one of them - select FMGo14 and the file will go to FMGo14. But even with this native method, You will have 2 versions
If You want only one version, You have to use a server - or synk via server or via a client..
It's too bad that Go can't be like Kindergarden where kids learned to share the sandbox.
It's iOS. Security feature. Prevents any app from stepping on any other app's storage space.