how do you teach the difference between swing and the dotted eighth-sixteenth rhythm pattern
In my experience, you need to hear it. The two rhythms (triplet swing, and dotted quaver-semiquaver) seem quite similar, but different once you hear them. Trying to count the difference whilst playing is a recipe for confusion.
Note that I'm assuming there isn't a marking making the two notations identical. Sometimes the dotted quaver-semiquaver marking implies a triplet swing, but not always.
So, I'd pick a couple of good recordings, or play the various rhythms to a student myself. You have to feel the swing for it to work. I'm aware that sounds rather nebulous, but I don't think you can effectively count it. To me, the dotted quaver-semiquaver rhythm sounds more abrupt and jerky. Almost like you try and play the semiquaver on the start of the next beat, but not quite. An example which (unfortunately) comes to mind is the vocal riff at the start of Uptown Funk. You may have less annoying examples.