No, neither scenario is bartering. Bartering would be Person A does plumbing work for person B. In exchange for the plumbing work, Person B gives Person A horse. If you are exchanging money, it is not bartering.
If you are simply trading dollar for dollar, this is not a gift. You are simply exchanging money so you can use the currency in a different country. This is done every day when one enters a country with a different currency, but it does not create a taxable transaction. A gift would be you give something and get nothing in return.
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