The 31mm unmounted filter is just glass and gives you a 31mm optical window for the camera to see through.
The 1.25" filter has the threaded mounting which reduces the optical window down to 26 - 28mm (depending on the manufacturer).
To reduce any vignetting the 31mm unmounted is better but there can be confusion as to which way they are installed. (shiny side towards the scope, dull side facing the camera ??)