It's not the same as a disagreement (10)

I believe the answer is:

difference

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'disagreement' is the definition.
(I know that difference is a type of disagreement)

I don't understand how the remainder of the clue works.

Can you help me to learn more?

(Other definitions for difference that I've seen before include "Change" , "Discrimination" , "Quarrel; remainder in subtraction" , "Diversity" , "Variation" .)

I've seen this clue in The Globe and Mail and The Irish Independent.

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