To me a variety is a die issue, not a strike issue or a coin issue. When a coin has a doubled die, then the hub process is incorrect when the die was hubbed. How many of these can happen? Few if they catch the die early. (IE the 1958
DDO, only three known so far) of a larger number that could be in the thousands (1955
DDO, only know up to the mod die states) or a million plus if the die was used from a full run. That is what I call a variety. There are other types of varieties.

RPM (Re-Punch-Mintmarks)

RPD (Repunched dates on the 18th and 19th century coins) Also

OD. (Over date with a different year used)

OM (Over Mintmarks A different mints punched was used over a previous mintmark locations punch)
To me that is the proper use of the term variety.
Some other uses of errors are called die events. As the die breaks down it can go though different events that happen to them and make some different looking coins. But they are not a variety, but a die event.

But one time errors are the unique finds. Check the list above in the box.
But a one time variety could not happen.