To my mind, there is a clear difference in pronunciation between the two: the em-dash is a clipped break, or a very abrupt shift, while the ellipsis is a distinct pause with a bit of elongation of the prior syllable.
If you take a sample sentence of
Wait... there may be something.
Wait—there may be something.
then for the first one, the word "wait" has a downward intonation, and a slightly drawn-out "ayy" sound; and there is a clear pause, possibly a full inhalation, before starting to say "there". It tends to have more of a connotation of thoughtfulness.
For the second one, "wait" is more emphasized, with no downward intonation, and is somewhat clipped; there is still a short pause before starting to say "there" but there is definitely no inhalation. It tends to have more of a connotation of urgency.