If the definition of dragon were purely based on morphology, then you'd be correct (mostly. Do wyverns often breathe fire?). But considering the definition of dragon [i]within the universe[/i] is what you see, they still count as dragons, I'd think.
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Wyvern can breathe fire, but they more often are depicted as breathing poison and also have a barbed tail. Dragons also are a lot smarter than wyvern as they can speak.