Images of dragons in eastern v. western culture

Question spawned by a late-night discussion:

Dragons are present in both Eastern and Western folklore. We have the brave Knight going off to slay the dragon and rescue the princess in Western cultures, and we also have spirits taking the form of dragons in Eastern culture. In eastern cultures (forgive me for any inaccurate generalizations, please), dragons are symbols of good luck/fortune, etc, while western cultures depict them as the enemy - mean, evil creatures to be feared. The visual depiction is different, too - the long, serprentine, and unwinged creatures of Japan and neighboring nations, and the dinosaur-like, winged creature of western legends.

Which came first, or did they two ideas evolve seperately in their respective areas? If so, what is the likeliness of two cultures developing such similar mythology?

I’m not sure whether there is sufficient ground for comparison.

What exists is actually, in my opinion, two different mythological beings that are physically different - as the OP has pointed out. It just happens that translators have opted to call the East Asian creature “dragon” as well, thus creating the idea that these two have some similarity.