They're ways to solve two different problems. The goal of application development is to make a user happy (for some value of happy), and the goal of software engineering is make a good system (for some value of good).
Hmm never thought of it that way. So being an application developer has a more direct tangible effect on the end user as compared to being a software engineer. By that definition then most startups are built by application developers. I guess I know where I'll be specializing in from now on.
