I know nothing about Canadian whiskey, but the difference you mention between Irish whiskey and scotch is exactly right. It's because scotch is distilled using burning peat as a heat source, which imparts that earthy, smoky flavor. Irish whiskey is distilled over a gas flame, so the fire has no impact on the flavor. I imagine distillation of Canadian whiskey is also heated by natural gas.

According to Wikipedia, Irish whiskey is predominately distilled from barley while Canadian whiskey is mainly corn. Canadian used to be mostly rye, however, which is why some uninformed souls use the terms "Canadian whiskey" and "rye" interchangeably.