Simple starting answer: Canada (for the most part) only taxes income, not 'money you have.' Of course, if you have significant income from savings, investments, and property on an ongoing basis (incl capital gains and the like), you will pay taxes on those. Generally speaking, taxes paid in other countries are credited in Canada - but since tax rates (and basis for defining income) can be different, as are other deductions, you may or may not end up owing some to one country or the other.
When you begin to pay taxes on income on a move to Canada, timing may make a difference how much you pay.
If one has 'a lot of money', then it would be stupid not to use some of it to consult a professional.
And no - renouncing Canadian citizenship will usually not affect how much taxes payable in Canada - Canadians (incl PRs) pay taxes based (mostly) on residency. The reverse is not true for US citizens.