Up until a couple of months ago, I wasn't able to put it into words myself.  One thing I knew was the overlap especially when it comes to web design and user interface design for web applications.  So what's the difference?

After Google-ing it and pulling up the Wikipedia post on user interface design I came across this sentence:

Where traditional graphic design seeks to make the object or application physically attractive, the goal of user interface design is to make the user's interaction as simple and efficient as possible, in terms of accomplishing user goals

This statement is referring to graphic designers and not web designers.  However many graphic designers have transitioned to the web and uphold their objective of creating visual attractive sites.  Some web designers specialize from the angle of design in new media such as flash, music or video and their goal is a higher level of visual and emotional impact. Regardless of whether the web designer has graphic or interactive design origin, the important distinction is that primarily, web designers are not focused on making user interaction as simple and efficient as possible in terms of accomplishing user goals.

I am entirely buying into this distinction.  It is this distinction that made me realize that I am a user interface designer.  

I went through wikipedia history and traced the origin of this statement, to the author who goes by CatCubed.  Thank you CatCubed for defining this distinction!