The second one makes sense, there the camcorder is being the slide show and the recorder is just recording whatever it outputs, no special function of the recorder is involved.
But for the first option, "Copy to DVD" for a JPEG file, does that really make a DVD Video out of the JPEGs, i.e. playable in a standalone DVD Player? If so, wouldn't you need to tell it things like how long to pause at each picture? Bear with me as I am just trying to figure out the extent of this feature.
EDIT: Just saw your edit about "Once on a DVD". Have you tried playback of such DVDs on a regular player?