The difference between a mint error or variety is a mint error occurs during the planchet or striking division of the minting process and a variety happens during the die division of the minting process. So a mint error is a malfunction or human error when the equipment is not adjusted proplery or a malfunction occurs.
During the planchet division errors like extral metal rolled into alloy stock or clipped planchets occur, during the striking division is can be a multitude of errors can occur and here's just a couple. Capped Die, struck though foreign object, brokage strike, and multiple strike and many, many more errors can occur in this part of the minting process.
A variety is a bit different because it occurs during the die division of the minting process and is an intentional or "unintentional" change to the design or face of the die. Examples of a variety are doubled dies (not doubling or maching damage), repunched mint marks, missing mint mark, or any occurance that actually changes the design in any way on the die that strikes the planchets.
One other and major difference is a variety will have many examples that are exactly the same, meaning someone found so many with the same die difference and they became attributed as a variety. A mint error is different from this because it is unqiue and does not involve a change to the die design itself.
If you want to learn more about mint errors and varieties and see what they look like then visit our US Mint Error Page
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