As I have seen lots of interest around this answer, more precisely around the number of legs (as @lfurini said), I have decided to open a question to find a canonical answer.
From the discussion (answer and comment section), one can see that the creatures are different, even though, as @jwenting pointed out:
for a long time the terms dragon and wyrm were used interchangably in English.
And from this answer one can find an effort to give standard definitions for them.
However, when it comes to specifics, more precisely the number of legs, there seems to exist lots of interpretations.