And for visual learners:
http://www.youtube.com/watch?v=LRTlm_cKZ8Y
What you see them wrapping around the cylindar on the sending end is the Original / Type 1 / News / News Service / Press photo, and what is produced on the receiving end is the Duplicate / Type 3 / Wire Photo.
One thing to keep in mind though, as David alluded to, is that MANY sellers/dealers/auction houses misuse the terms, so you have to be careful. If you're on the buying end, knowing what "tells" to look for is often much more helpful than relying on the seller's verbal description. I've seen original photos from the 1910's described as "wire photos" (impossible, because the process hadn't been invented yet), wire photos with the caption embedded in the front image described as "Type 1 Original," glossy modern prints with "VINTAGE" in the title, etc. Many sellers will just treat these as "keywords" that they throw into the title and description willy-nilly to try and grab your attention and get their items to turn up in your searches.