This of course pokes fun at me as much as other webdevelopers. It’s currently what I do for a living.
I haven’t really encountered this rivalry in a real sense. Most of it was just amusing banter. Unlike the occasional wars between developers and designers. But I do feel that webdevelopers and application developers work on different levels.
Coders usually work very deep inside the core of languages. Spelunking away at memory management, pointers, parallel processing, etc.
Whereas Webdevelopers are more digging away at the surface letting such deep things to the scripting engine they chose to use. Of course webdevelopers are often more required to be aware of design aesthetics and most coders want nothing of that sort.
Of course the lines are fading ever quicker with development tools becoming more and more accessible to use. So who knows what coders or developers call themselves in times to come.