A variety is a type of coin that can be repeated more that once. So would die clash be considered a variety?
Most of the time they are not real interesting. But every once in a while they do catch some attention. But rarely. A variety is usually a coin that started out with a hubbing error, or miss puched mint mark, 19 century overdates, over mint marks. They start off with the design from coin one. I know others view other events as errors. But I'm a purist on the term variety.
What constitutes a variety, and what constitutes an error, is a battle that has been going on among numismatists for generations and will still be going on for generations more. So to answer your question, it depends entirely on who you ask
Not all coins struck by a particular die that has clashed at one point will have the clash. Clashes can occur at any die state...early, mid, and late. That means you can have a normal coin and a clashed coin struck by the same die because one was struck previous to it becoming clashed, and the other was struck after it clashed. In this sense, because not every single coin struck by that particular die would show the anomaly, I would call it an error rather than a variety.
I tend to think of clashes are neither errors or varieties, but rather as die states since they can come and go. That being said, however, the clash die state may not correspond to the die wear state.
That's why I said die stage and not die state. Die state tends to indicate the amount of wear the die has had, die stage indicates changes that have happened to the die such as cracks, clashes, polishings etc.
According to the "The Official American Numismatic Association Grading Standards for United States Coins" on page 346; Clash marks are impressions of the designs of the obverse and the reverse onto a coin. This is damage, and is caused when the striking dies impact each other with great force without an intervening planchet. Then the damaged dies, then transfer the results to the next planchet. On page 351; A variety is a minor change, or die difference, within a basic type design of a coin's die surface. When the defective dies are found, they are repaired or replaced. I hope this helps.
Folks will never agree on the topic. The Cherrypickers Guide to die varieties has a few clashed coins listed.
A variety's origins are traced to the die manufacturing process. A die clash origins are traced to the coin manufacturing process.