(I have edited your query, since only one question is allowed per post.)
There's really no comparison when it comes to the sizes of Hudson Bay and Lake Superior: The second largest bay in the world, Hudson Bay is vastly larger. Hudson Bay is more than 850 miles long, compared to Lake Superior's 350 miles. Hudson Bay comprises 470,000 square miles, while Lake Superior is less than one-tenth that size (31,820 square miles). One of the largest fresh-water lakes in the world, Lake Superior is somewhat deeper, however (1332 feet maximum to Hudson Bay's 330 feet). Hudson Bay drains an area of nearly 1.5 million square miles compared to Lake Superior's water catchment area of 49,305 square miles.
Lake Superior is the largest of the Great Lakes and the third largest freshwater lake in the world. Its surface area is 31,700 square miles or 82,170 square kilometers. The Hudson Bay, however, is not a separate lake but a kind of inland sea. It is second (in bays) in area only to the Bay of Bengal with an area of 317,501 square miles (822320 km). Therefore, the Hudson Bay is about 10 times the size of Lake Superior.