Yeah, you're right, but they're a different type of Dragon. A Lindwurm, a Knucker and a Lung are also dragons, but a different type.
If you just say 'Dragon', most people simply think of the "European Dragon".
So, while still being a dragon, since the European Dragon has no other name to be called by, it's easier if this type is called by it's name, Wyvern, to forestall any confusions.
(I hope, it's still understandable what I mean. I'm not too good at english, please forgive me for bad grammar or weird sentences.)