Um... No, generally a game exploit will be a glitch in the game's client that allows you to do something you shouldn't be able to do. In the case of the infinite bank exploit, it's both client sided and server sided. Because the server isn't checking whether your bank is full when you're sending the swap packet, and the client lets you send a swap packet with only one item.
Server sided vs client sided doesn't really apply anyway, those are generally terms used to describe hacking/exploiting that either does or doesn't work in an online game. An example of a client sided hack for aqw would be changing your name or the visible amount of gold you have. The infinite bank exploit does affect the server so it is basically a server sided exploit, but it's using the client because aqw isn't good at preventing that sort of thing due to the limitations of flash.
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