Being a Double Die Error is what makes a coin an Error Variety. Not all errors are varieties and not all varieties are errors. Some varieties are errors and some errors are varieties.
Now, for the Nth time, I will post this link to Wexler's works, one of the 3 top error/variety experts with formal journals/studies/publications that are universally accepted. Go to the bottom to see examples of each type of "doubling" and then a laundry list of varieties/errors on the long left side: https://doubleddie.com/144801.html