That's all well and good, but when the waitress at Morimoto's explains gyoza as a pot sticker to the couple from Wheeling, she's doing it because it's a catch-all that everyone can understand.
I get what you are saying here, but understand that if you oversimplify things you can lose the nuance of what you are actually getting to eat. The waitress may be simplifying for you, but she is also under serving you with information. She could easily say they are similar to a potsticker, but have these specific differences.
Much like if you asked what type of beer they had on tap and they told you "We have thirty five taps, they are all beer, which would you like?" you would have no more information upon which to order.
When someone says "Potsticker" my mind conjures up a simple image of the frozen ones you can get at costco, that really aren't that bad, but when you pay 7.99 for six of them at a restaurant you feel like you may be getting the shaft a bit.