In the UK, whilst most people will understand that 'Asian / Chinese' dumplings are some kind of food, wrapped in dough, plain-old dumplings are something else far more ordinary.
A dumpling, in the UK, is a ball of self-raising flour and suet (shredded hard animal or vegetable fat) bound with water, which is cooked in a stew, so that it takes on the flavour of the dish and becomes light and fluffy.
So, to directly answer your question. I would say that whilst your teacher was correct, in that the English-speaking world would call 饺子, 'Dumplings', I think that's simply because that's the nearest match we have. It is not a catch-all word for every dish which consists of dough / pastry with a filling.
As an aside, IMHO, beef stew & dumplings is one of the finest dishes in the world!
