They are actually completely different creatures - it just so happens that their names are translated to the same word.

The Chinese dragon, for example, is said to have the body of a serpent, the head of a lion, the antlers of another mythical creature, and is a spirit of rivers and waterways.

The European dragon, on the other hand, is made up of ... well, all kinds of creatures. Bats, and snakes, and so on. It's often associated with poison, or fire, and shadows.