Like Daryoush said, I can't stress enough the importance of contacting a customer with this sort of disrecpancy .
Realize that if you lived on a different continent than the associated credit card, you'd likely be a bit understanding if you ordered something and a merchant elected to confirm the purchase with you. Just apply this sense of reason to the customer. :D
Also understand that fraudsters frequently employ the same tactics repeatedly. If this pattern reminds you (or Shopify) of previous fraudulent patterns, then this information coupled with the disparity in billing and shipping addresses raises several red flags.
I don't think you should accept this payment without clear confirmation from the customer. Good luck out there!