Do notes have plate varieties similar to die varieties on coins? Or are the plates much tougher with a longer life to not need as many changes, etc?

My assumption would be that the only variety on the plates would be signatures....... Unless there is a redesigh of the note itself......

The other variations are just the coloring of the notes.......

but plates are like dies, they probably have a master engraved die that engraves the plates...

Yes there have been some cases. For instance, one of the Phillipines note had the spelling of President Arroyo wrong and now it is classified as an error note.

There is another example with Kazakhstan recently, perhaps back in 2005 or last year that with the 2000 and 5000 tenge, the notes were accidently printed in Russian letters instead of Kazakh letters. It was noticed right away but however both of them circulated at the same time as you know, Kazakhstan used to be part of Russia and claimed that Russian is also part of their identity. Obviously Kazakhs were outraged over this reasoning. It's more like the authorities didn't want to waste time and resource to pull out the notes that were already released.

I can't speak about other countries or types, but there is often quite a bit of variation on Confederate notes, particularly those which were printed by lithography. Bradbeer, Criswell and others cataloged a number of varieties. More recently, Fricke published the research of the late Dr. Douglas Ball. Varieties include significant plate differences, series, paper types, watermarks, plate errors and printing errors such as inverted backs. Not all plate differences are cataloged, however.