The key differences between muffins and cupcakes
1 - Icing
If it has icing on it, that's a cupcake!
If it doesn't, that's a muffin, and why would you ever eat that?
2 - Presentation
Well, one thing about the presentation is that the cupcake, the one worth eating, is presented with icing all over it. But we already discussed this in point #1.
Some further details of presentation, however, are that a tray of cupcakes will be presented by someone who is smiling (you will also be smiling, because of cupcakes), and is excited to give you this food. Perhaps they will say something like, "Happy birthday!" or "Surprise!!" or "Surprise, happy birthday!!!"
A person giving you muffins (on a tray or a plate, doesn't really matter, not important, they're just muffins) will be saying something like, "Yeah, they're over there," gesturing vaguely. Nobody's too excited.
Probably they'll add something like "eat as many as you want. Trying to get rid of them." All part of the trademark muffin presentation.
3 - Flavour
Cupcakes are enjoyable to eat because they taste good. Muffins are not enjoyable to eat, because they do not.
I can already hear you protesting right now: "But wait, I loooove my morning carrot cake/blueberry/morning glory muffin."
The difference lies not in definition but in degree. We're actually on the same page: the simple rule is that if a muffin tastes good, it's a cupcake. And would be even better with icing on it.
4 - Shape
If it is almost finished and is slightly compressed because it's being held in someone's hand, that's a cupcake.
If it has maintained its full original shape, or has had one bite taken out of it before being placed back down on the table (or is just the top — have you ever heard someone say "I'll just have the cupcake top, thanks"? No. They want the whole thing), that's a muffin. And it's going to stay that shape because ain't nobody touching it. So if you're into consistent shapes that become more consistent by the minute, go for the muffin.
If you like food, though, cupcake. Definitely go for the cupcake.