There are classifications for Master Hub Doubling, Master Die Doubling, Series Doubling (for years and denominations where multiple masters were in use), Working Hub Doubling, and of course, Working Die Doubling which is commonly referred to as a "doubled die".
Machine Doubling,
Die Deterioration Doubling, repunched mint marks, and true doubled dies are all separate types of doubling that have distinct causes. The first two are essentially worthless; the last two can add considerable value. It is quite common for vintage coins to exhibit two or more of these phenomena.
There is a very excellent article on the Wexler files website that explains the whole process of manufacturing the dies used to strike coins. I have re-read it many times, and I highly recommend it.
http://www.doubleddie.com/58201.html