Can a Canadian receive money from a US (taxes paid) source without it being taxed again?

If I receive money from an American relative on an annual basis and tax has been paid on the funds in the US as US earnings, is it taxed again as earnings by me as a Canadian recipient? If so, why? Wouldn't it then be double taxed? Could it be considered a monetary gift if received on a regular basis and not claimed as a tax deduction at the outsource?