Programmer Engineer?

Title says it all. It seems confusing doesn't it? This is my new job title when I graduate. I've been working as a software engineer intern for the past 2 years at a large corporate company in Massachusetts. I received my job offer and to my surprise, the title is Programmer Engineer. HR says the internal title is Software Engineer. So what am I? What should I put on my resume?

Now wait, can't I just ask HR about this? Yeah... but I want your take on it.

To me it seems a bit convoluted since I don't engineer programmers. Would it make sense to refer to my position as Software Engineer when I apply elsewhere down the road? Any thoughts?