We share the Beaufort Sea with the USA, but our continental shelf is about twice as wide as theirs, so there.
Demarcating the boundaries of oceanic bodies of water is more of a naming convention than anything else, at least in this case.
The Beaufort Sea can be taken to include the whole of the clockwise gyre of the Canada Basin of the Arctic Ocean north of Alaska, Yukon and the Mackenzie Delta coast, bounded on the east by Banks Island and Prince Patrick Island. Alternatively, it has been defined as that part of the Arctic Ocean lying south and east of a line connecting Point Barrow, Alaska, and Lands End, Prince Patrick Island. – The Canadian Encyclopedia
The Mackenzie River (which in North America is second only to the Missouri/Mississippi Rivers in length) dumps significant amounts of water and sediment into the Beaufort.
Annually, about 300 km3 of freshwater and 85 million tonnes of sediment pass through the Mackenzie Delta to the Canadian Beaufort shelf.
Opinions vary about the ecological significance of the Sea. On the one hand . . .
More than 70 phytoplankton species are found in the Beaufort Sea, but the total biomass is not large. Nearly 80 zooplankton species have been found, and the bottom fauna consists of nearly 700 species of polychaetes, bryozoans, crustaceans, and mollusks. – Encyclopedia Britannica
And on the other . . .
It’s home to abundant wildlife including fish like Arctic char, birds like the king eider, marine mammals like beluga and bowhead whales, and predators like the polar bear. Today, as it has for thousands of years, the Beaufort Sea supports the livelihoods and culture of the Inupiat, Inuvialuit and Gwich’in peoples. – WWF
Opinions do not vary about how damned cold it is.