"...somewhat different..." Yep. In North America, there is an international agreement between Canada, the U.S. and Mexico about migratory birds. In Canada, it's called the Migratory Bird Act. Covers seasons, mag capacity(3 in the gun only) and licences, etc. Without looking, I think it covers bore size too. Not that I'd put any money on that. I think the Act states a minimum 20 guage/bore, but I'm guessing.
In any case, 4 bores are extremely rare, expensive and, I think, too big, legally, for migratory birds in North America. Do a net search for 'punt guns' and 'market hunting' for better info.
In the late 19th/early 20th century, market hunting(literally hunting game for sale) was made illegal. A 4 bore, I think, is one of the bores considered to be a market hunting bore/guage. Evil, so it is. A 4 bore rifle is fine assuming the shooter is a bit nuts.