The books in the Kobo Desktop app are in a special format which can only be transferred to a Kobo reader.
To use your Kobo books on the Nook, you'll have to download the ePub/PDF versions (not all Kobo books have them) and sideload them using ADE, just like library books.
Just login to the Kobo website and under your "Library" next to each book you have that you paid for or added when it was a freebie, you should see a blue "Download Adobe DRM ePub/PDF" button. Click that to download the .acsm pointer file which you then open using ADE to download the real book to sideload onto your Nook.
ADE keeps the downloaded files in Documents/Digital Editions (possibly My Documents on Windows), by the way.
Hope this helps, and welcome to MobileRead!