I'll offer you my view on this which may vary from other's:
Software Engineer/ Programmer:
This is rather broad. It basically covers the whole industry of software technology. I worked as a control systems engineer after college writing relay ladder logic software for programmable controllers. I considered myself a software engineer, but that job hardly related to what I do now as a .NET developer. However, I think both would fit under this title.
Application Programming / Maintenance:
This is another ambiguous title. An "Application" could mean anything. Google mail is a web based application, Google Earth is a desktop application. However, the two are worlds apart from a programming skill standpoint. So this isn't very descriptive a title.
Yet again, another ambiguous title.
Embedded / EDA / VLSI / ASIC / Chip Design:
This one is far more explicit and specific. While I don't know what all those abbreviations are, it certainly hints toward very specific areas of technology.
As far as jobs relating to skills found in an ASP.NET curriculum, the first two job titles would be applicable. Maybe not so much for the third, and definitely not the last. I would be surprised to find anyone working at the embedded/chip level using .NET seeing as the .NET framework is a operating system based framework. (Do they have a linux kernel that will run Mono on a 64HC11 yet? ;))
The important thing to look for is the job description. The title is usually meaningless without more detail. Look for listings that discuss the technologies that you know (ASP.NET, C#, etc.).