The diplomatic missives include:

A torn-out Bloomberg Businessweek cover featuring a portrait of Justin Trudeau.

A back-and-forth about U.S.-Canada trade figures that culminated in Trudeau sending Trump a printout of the website of the Office of the United States Trade Representative with a smiley face beside the U.S. government figure showing America has a trade surplus with Canada (contrary to Trump's claims).

Context: The May 1–7, 2017, issue of Bloomberg Businessweek — featuring a picture of Trudeau headlined "The Anti-Trump" — caught President Trump's attention, according to 4 sources with direct knowledge. Trump tore the cover off the magazine and wrote on it, in silver Sharpie, something to the effect of "Looking good! Hope it's not true!" according to these sources.

Before the White House mailed this diplomatic correspondence, it went through the normal clearance process inside the National Security Council. While some White House staff thought it was not the appropriate way to communicate with a foreign leader, they ultimately figured "it was done in good fun and would be interpreted as positive outreach," said a source with direct knowledge of what happened. So the White House mailed the magazine cover to the Canadian Embassy in Washington.

it went through the normal clearance process inside the National Security Council. While some White House staff thought it was not the appropriate way to communicate with a foreign leader, they ultimately figured "it was done in good fun and would be interpreted as positive outreach," said a source with direct knowledge of what happened. So the White House mailed the magazine cover to the Canadian Embassy in Washington. The Canadian ambassador thought it was a prank, according to 2 sources familiar with the situation. He called the White House to check, and a White House official confirmed to the ambassador that the note was real, one of these sources said.

Months later, on Dec. 8, 2017, President Trump falsely told a rally crowd in Pensacola, Florida, that the U.S. has a trade deficit with Canada. Around that same time, Trump also mailed Trudeau a document purporting to show that the U.S. had a trade deficit with Canada, according to a source with direct knowledge.

Trump wrote in Sharpie on the document: "Not good!!" or something to that effect, the source recalled. Trump's document only mentioned America's deficit in the trade of goods and ignored its surplus in services (the two combined would gave the U.S. its overall surplus).

A few weeks later, Trump received a handwritten letter from Trudeau. The note, on Trudeau's official stationery marked by the Maple Leaf, began with a friendly tone, but ended with a drop of acid.

"Dear Donald," Trudeau wrote in the letter dated Dec. 20, 2017, according to a source with direct knowledge of its contents, which 2 other sources confirmed. "It's been a busy year! Enjoy the Christmas holidays — you deserve it."

"One thing," Trudeau added. "You gave a great speech in Pensacola, but you were slightly off on the balance of trade with Canada. USTR says so! All the best for 2018, Justin."

The second page of the letter brought the kicker. Trudeau enclosed a printout of Canada's informational page from the website of the Office of the United States Trade Representative.

Trudeau underlined the section on the USTR website, which at the time reported that "the U.S. goods and services trade surplus with Canada was $12.5 billion in 2016." Trudeau circled the $12.5 billion and drew a cheeky little smiley face next to it, according to a source with direct knowledge.

A Canadian government official responded to this reporting: "We're not going to comment on whether or what paper was exchanged between our 2 countries. There was a lot of back and forth. That said, it is certainly true that there were disagreements between our 2 countries about the figures, and we repeatedly pointed to USTR and U.S. Commerce's own figures. On your second point (the Bloomberg cover), no comment, but we don't deny it."

Why this matters: The U.S.-Canadian relationship is, in normal times, low-friction. But not under Trump, who views Trudeau as an irritant at best. In a conversation in the White House last year, Trump told aides he thought Canada was "the worst" country to negotiate with. "Who would think? Canada?" Trump said.

Trump now says very little about Trudeau, according to an adviser, and believes he and his trade representative Bob Lighthizer got the better of the Canadians in their trade negotiations.

Behind the scenes: Trump privately refers to Trudeau as a "wise guy," per sources with direct knowledge. He describes Trudeau as young and cocky, and he resents it when Trudeau comments on American politics.

Trump has gleefully recounted to aides how he threatened the Canadians with auto tariffs. He says it got him a better deal on the U.S.-Mexico-Canada Agreement.

Trump has also privately described Canada's Foreign Affairs Minister Chrystia Freeland as "very nasty," according to senior administration officials.

Trump was pleased with the optics of the G7 last year, an adviser said. Trump says he dominated Trudeau there, the adviser added, and loves the viral photo of himself sitting with his arms crossed as world leaders hover over him. Trump also relished leaving the summit early — snub to Trudeau, who Trump said had treated him with disrespect.

The White House did not respond to requests for comment.

The big picture: The president is in Year 3 of his relationships with foreign leaders, and in some cases they've changed substantially. Trump's bromance with France's 41-year-old leader Emmanuel Macron has faded, and Trump privately places Macron in a similar “wise guy” category as the 47-year-old Trudeau.