Why du and df show different disk usage values on Linux

If you do a df, and you compare those values with du, it is possible that the values don't match. There are multiple reasons why this can happen, and one of those reasons is that files were deleted, but the files are still in use by an application.
In that case, it is possible that you need to stop/restart the particular application. This of course depends on the application itself.
With lsof you can see if you have such a situation where an application is still 'locking' that space, and it will show which application is causing this.
Below is an example:

machine:/ # lsof | grep "/mymount" | grep deleted 
  myapplication 51789 root 3r REG 254,4 526066393088 6466832291 /mymount/backup.dat (deleted) 
  myapplication 51789 51791 root 3r REG 254,4 526066393088 6466832291 /mymount/backup.dat (deleted)