Hi Kristen,
The app won't allow you to browse songs as either standard or Nashville chords. You would have to transpose (change the 'from' and 'to' chord types, but leave the transpose key the same) for each song. Again, this will only work if you have specified the correct key for the song already.
If you want to have two different sets of song files (one in standard and one in Nashville format), you should copy the required songs into a new subfolder - I'd recommend using a file manager app on your device for simplicity. E.g. if your songs are currently in the 'MAIN' folder, create a new folder in the OpenSong/Songs/ folder named 'Nashville'. Paste the copied songs into this folder, then start the app and allow a full index.
Once the app opens, open one of the songs in the Nashville folder and assuming you have set the song key and want to convert them into Nashville format, click on the transpose page button set the options as shown below - note the detected and new chord formats. Don't change the key. If you see the number 0 instead of the key, you need to set the key in the song edit page before trying to convert.
Original song:

Transpose button:
After transpose:
Hope that helps?
Also, if you are simply trying to transpose in the setlist, the setlist does not store the chord display type unless you create a variation item for the song. If you wanted to do this, keep your songs saved in the normal format in your OpenSong/Songs folder and add them to the set. Then transpose the items in a similar way, but switch on the 'Make a set item variation' option.
Variation files are saved to the set file and get loaded back in when you load the set again.
Gareth