To "swap" means to trade one thing for another example: She swapped her drink for mine. To "change" means to modify or make something different examples: She didn't like her pants, so she changed into a dress. I changed my answer on the test. A "change" is not a trade... you can change something to be completely different.

I'd think the synonym for "swap" is "exchange"(not simply 'change'). "Swap" is for common daily use, and "exchange" is more for business/formal transactions. "I'd like to exchange some dollars for euros" "It doesn't work? Take it back to the shop and see if you can exchange it." "I'm originally from Australia, but I'm here in California on a student exchange" (I like Srgause's "swap" example, so I won't add any more. ^^)