(a) Yes. (b) No.
Most of the time. In Canada the Federal Government and Provincial governments have unified income tax payments in most of the provinces.
What this means is when Income tax is collected from you the taxpayer some if it goes to the federal government and some goes to the provincial governments. This is not the same as transfer payments (see next week for more on transfer payments). This is more simply described as unified billing. Instead of getting two income tax bills, you get one income tax bill and the governments allocate the amount based on the formulas on your income tax return.