The backup file created by the 'Backup' function will save the files (styles included) on the USER drive of your S770.
When you 'hit Restore' on your new S775, the keyboard will look for an S775 backup file (probably named 'PSR-S775.bup').
Because the backup file on your USB is for an S770, it will be called 'PSR-S770.bup' so the S775 won't find the file!
You could try changing the filename to 'PSR-S775.bup' but although the keyboard might then list it, I think that if you select it, the keyboard will display an error since the backup files have internal headers which identify the keyboard model, and anyway the parameters saved in the file may be different!
If you have copied the styles in the S770 USER drive to a USB stick, then you can add them to the USER drive on the S775 by using the standard file management functions Copy/Paste. If necessary, you can read how to do this in the section 'File Management' starting on page 27 of the 'PSR-S775 Owner's Manual'.
Once you have copied the styles etc. to the USER drive of the S775, you can then create a backup file for the S775 if you like, which you can use on another S775 in the same way that you did with the S770s, but I doubt that this file would work on a S770 if you still have them!.
However you could simply keep all files on a USB stick and run them from this instead, and then you could move that from keyboard to keyboard irrespective of the Yamaha model.
Regards
Ian