First thing to realise is that they are totally different and have no relation what so ever
Duplication is when a backup is copied (duplicated) so that you have a second copy of the backup (maybe the first is on disk and the second is on tape - but they are identical copies, just in a different place.
De-Duplication is, as has already been described, used when you perform a backup to a special de-duplication disk area and the data written identifies things that are the same so doesn't need to write all of it to disk.
So as your write the data if you back up a Windows 2003 Server the data is stored, although some parts of its system may have duplicates so not all have to be backed up - if you then back up another 2003 server the disk areas has seen most of the files before so doesnt need to hold them again and just keeps a record of them
This saves a lot of disk space and in some cases you can back up a whole server but not need to actually write anything extra to disk as it has all been seen before
Hiope this and the other excellent replies explains it for you