They really aren’t the same. I find it highly unlikely that any human has ever seen a dragon that breathes fire and has wings.
See this thread: Where did the idea of dragons originate? - Factual Questions - Straight Dope Message Board
According to Daniel Cohen (Encyclopedia of Monsters, 1982), the oriental dragon and the western one have wholly independent origins. (Although similarities between the 2 creatures led Westerners to originally speculate that they had a common origin.)
Western dragons were portrayed as evil, and were thought to be based upon the serpent (or “worm”). As a simple snake (albeit a large one) was not thought to be a sufficiently intense symbol of pure evil, various appendages were added over time. Hence, the breathing of fire, the wings, the feet etc.
There are reports of stuffed baby dragons from the middle ages, which cynics suggest resemble bat wings sewed on lizard bodies.
Certain monks were reported to have displayed the remains of a seven headed dragon, which may have resembled seven weasel heads sewn onto a snake’s body.
While oriental dragons are long and fearsome, they were also portrayed as guardians of great fortunes; sometimes they were thought to hand out gifts. Usually (not always) they were benevolent, symbols of royalty and good luck. They often lived in lakes or rivers. Their provenance is thought to be quite different: they are probably based upon the Chinese alligator, since the snake was also thought to be evil in China.
Both the Chinese and the Europeans saw departed dragons in the fossil bones of certain extinct creatures.
Point 3 is controversial, and was discussed in the linked thread. Point 2 provides an evolution of Western draconic folklore. Notwithstanding the claims of Peter Dickinson (h/t Tuckerfan), I’m highly dubious that any creature larger than a human that coexisted with Europeans could disappear without leaving convincing physical evidence.