Software engineer at Google. I primarily consider myself a web developer though.
The term "Web Developer" is a term with multiple meanings. It's kind of like the word "art." Art has multiple meanings. The "low" meaning is "skilled visual craftwork." The high meaning is "that which exposes your inner humanness. That which a machine could never do."
The low meaning of "web developer" is "some web designer who learned a bit of PHP. A hack, essentially." The high meaning is "one who uses whatever means necessary (coding, graphic design, whatever else) to present web user interface."
By this definition, I'm web developer in the finest sense of the word. However..... along the way I've become and awfully good software engineer too. Let's just say I'm most passionate about web development but also have a natural aptitude for software engineering (less the release engineering and on-call stuff of course).