Americans who have legal residency in Belize are still residents of the US, so you they pay taxes in two countries—the US and Belize. If you are an American citizen, you have to pay US income taxes, regardless of where you live. There are certain exemptions that you can get if you reside out of the US for a certain period of time, but you still must file your US income taxes forever.
The situation is different for Canadians than it is for US citizens. For Canadians, residency and citizenship are separate. I am now a resident of Belize and I declared non-residency in Canada, so I do not pay taxes in Canada any more and the income I earn abroad is non-taxable. But if you have assets in Canada and you haven’t declared non-residency in Canada, even if you are already a resident of Belize, you still have to pay income taxes back in Canada. In order not to pay income taxes in Canada, you have to declare non-residency in Canada and you have to liquidate all your assets. You cannot even maintain a Visa or a MasterCard in Canada, let alone a residence of any kind or any assets.
As a Belizean resident, you have to pay Belizean taxes.