I'll start by saying Web developers are software developers, but they can also be so much more, mostly depending on the size of the company and the size of the IT department.
Now when I say IT department, I come from a company that has one IT division with a Web department in addition to networking, development, DBA, and production operations.
I head up the web department and the development department is mostly PeopleSoft developers. Me and my staff are responsible for creating Web apps including the databases that go with them and specifying the setup of the web servers, so we cross from Web development to DBA to sys admins. That's why we are in our own department, our skills span too many areas to fit in any of the others.
My point is that it really depends on where you are and where the skills are located to do the job.
For contrast, I've even been a places where the Web developers were part of the Marketing department.
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