If the customer says "let me see if I have change" I would assume they meant the coins that would match the cents on the total. If I buy something and the total comes to $6.27, I may hand the person a ten-dollar bill and then say that, and pull out 27 cents, so I get bills back instead of coins.
On the other hand, when you give back their change, you mean the total. If I just gave you a ten-dollar bill, my change is $3.73. If I give you the $10.27, my change is four dollars even.
So "change" has two meanings: coins, and then the difference between the purchase price and amount tendered.
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