Thats a tricky one. It is kinda both. Errors are all one of a kind. Varieties are all the same. Clashes are mechanical errors that create a variety. Im goin with variety/error.
Of course it wasn't made that way by design! I personally believe they are and should be called errors. Varieties would be die changes, wrong reverse, etc. For example, small and large dates are varieties.
I know it wasn't make that way by design. I believe that part was an error, but if the definition of a variety is that all examples look the same then variety also fits. Maybe a variety with an asterisk, a variety made by error.
To me a die clash is a error . Die clashes are caused from the dies clashing together, without a planchet to be struck .
Just for a reference, the Error-Ref website has listings of what is considered an error and what is a variety. http://www.error-ref.com/ A clashed die is considered an error. Doubled Dies are varieties.
A lot of folks call clashed die coins errors and say they should not be in the CPG. I won't argue it either way. I'm good with calling them an error and a variety.
I never thought about it, but you are right, doubled-die coins are not errors. They were official releases (like proofs without mint marks) from the mints that did not have flaws from the minting process like double-strikes, off-center strikes, clipped planchets, unplated blanks, laminated planchets, etc. I will have to spread the word and get people thinking differently.
I theory a clash could also be considered a variety if the definition of a variety and error given earlier is true. After the dies clash several hundred to thousands of coins could be struck before the dies are replaced, all showing the same clashing.
It is tricky. If you go by the definition of an error being something that happens during the strike, and a variety being on the die itself, you have to break it down further. For instance, a clipped planchett happens before the strike but has nothing to do with the die. That being said, I have to go with anything on the die before the strike is a variety. Clashes would be errors because they are damage after the die was put into production. Any strike after is just a coin from a damaged die, not a variety.