Why are Canadians called Canucks, and why are Americans called Yankees?

YANKEE - (Dictionary entry)
A native or inhabitant of New England OR of a northern U.S. state, especially a Union soldier during the Civil War OR of the United States.

The origin of Yankee has been the subject of much debate, but the most likely source is the Dutch name Janke, meaning 'little Jan' or 'little John,' a nickname that dates back to the 1680s. Perhaps because it was used as the name of pirates, the name Yankee came to be used as a term of contempt. It was used this way in the 1750s by General James Wolfe, the British general who secured British domination of North America by defeating the French at Quebec. The name may have been applied to New Englanders as an extension of an original use referring to Dutch settlers living along the Hudson River. Whatever the reason, Yankee is first recorded in 1765 as a name for an inhabitant of New England. The first recorded use of the term by the British to refer to Americans in general appears in the 1780s, in a letter by Lord Horatio Nelson, no less. Around the same time it began to be abbreviated to Yank. During the American Revolution, American soldiers adopted this term of derision as a term of national pride. The derisive use nonetheless remained alive and even intensified in the South during the Civil War, when it referred not to all Americans but to those loyal to the Union. Now the term carries less emotion except of course for baseball fans !!!

To deal with the Candian/Canuck part of this question:

'History
The term was first used in the 19th century, although its etymology (origin) is not clear. Some possibilities are:

kanata1 "village"
Canada + -uc (Algonquian noun suffix)
Canada + -inuk (Inuit for "man")
Connaught, a rarely-used term for Irish-French-Canadians.

Meaning
The Random House Dictionary says that: "The term Canuck is first recorded about 1835 as an Americanism, originally referring specifically to a French Canadian. This was probably the original meaning, though in Canada and other countries, Canuck now more often refers to any Canadian.' -from http://simple.wikipedia.org/wiki/Canuck

See also https://en.wikipedia.org/wiki/Canuck#:~:text=%22Canuck%22%20%2Fk%C9%99%CB%88n%CA%8Ck%2F%20is%20a%20slang%20term%20for%20a,originally%20referring%20to%20Dutch%20Canadians%20or%20French%20Canadians., but disregard the part about the Vancouver Canucks having won the Stanley Cup a few times (they never have).