Morten -
I think its easy to get wrapped up in words that have multiple meanings. In this case, I suspect that the meanings may have subjective interpretations.
The way I use these words, mounting refers to attaching the print to a support, while matting refers to attaching a second board on the face of the mount that may (or may not) actually overlap the print. That is - the mount is under the print, while the mat is on top of the print.
With these definitions, prints can be mounted but not matted, matted but not mounted, mounted and matted, or neither mounted nor matted.