Dana, I'm glad you asked this question because it's something that I didn't really understand.I knew it was "plain;" however, I had no idea what that actually meant. Your question caused me to stop and do a little bit of research on what that actually means.
Although I never really found a real definition that I could quote, I found a number of sites that gave a "vague" impression as to what it means.
Apparently, a "plain" x-ray is one that does not use a contrast medium, which is what you said. Other radiographic tools, such as a pyelogram or angiogram, use a dye injected prior to taking the x-ray.
The American College of Radiology makes the distinction between general (plain) and advanced radiology.
I sure wish I could actually give a specific reference; however, I was all over the world (literally) looking at sites trying to find a definition.
Hope this little info helps others remember it is "plain" and NOT "plane." 
Gaile