Veloy II and Focomat Ic share many common parts -- the neg carrier and condenser in particular. Both great enlargers.
As to the negative carrier being "full frame," it is on some instances, but not all -- when I print negs shot with my SLR, for example, I can usually leave a black rim around the image pretty easily.
When printing negs shot with my M rangefinder, however, I can if the neg was shot with a 50 mm lens or longer, but shorter lenses do not -- the image is actually larger. This is because leica rangefinder lenses -- especially older ones -- are really the physical distance from the focal plane that the lens says -- so it is close to the film, meaning the image, to fill the frame, must project out at a sharper angle from the central axis of the lens.
The most extreme is my 21mm super angulon -- its rear element is only a couple of mm from the film, and its image projects out to far that, on the developed film, there is no separation between the negatives, which means when I print I am cropping off a bit all around just because it is too big for the negative carrier's hole.