While Sharif's office has released a read-out of his conversation with Trump, the US president-elect's team has issued bare minimum information, triggering much bemusement both in mainstream and social media.
"We know that Pakistani Prime Minister Nawaz Sharif and US President-elect Donald Trump spoke on the phone Wednesday.
What was said during that call is what's at issue," CNN commented.
"After the conversation, the Pakistan Prime Minister's Office put out a statement directly quoting Trump -- a violation of diplomatic protocol -- in which he glowingly praised Sharif," the network said.
Readouts of phone calls between world leaders are usually written safely way in order to protect leaders from incidental
backlash -- like the one the Trump team put out, it said.
"They're dry and diplomatic statements summing up conversations using carefully chosen buzzwords," it said, adding that such calls themselves are usually quite formal.
"A president wouldn't gush over a foreign leader the way that Donald Trump did. He wouldn't volunteer to do all these
things," says CNN political analyst David Gergen, who has served as an adviser to four presidents.
"Our relationship with Pakistan is one of the most sensitive and difficult relationships in the world. It's an extremely important relationship."
When making that call, a president would likely have a press aide and national security advisers at his side, according to Gergen.
"You'd carefully think through any call like that, you'd make your two or three points, [then] over and out," he said. "Especially don't leave them in a position where they could put out something so gushing that it hurts your relationship with India."
The Washington Post, in its report on the Sharif-Trump conversation, said, the Pakistani readout is "unusual in that it focuses almost entirely on Trump's contributions to the conversation, and reproduces them in a voice that is unmistakably his."
"Lavishing praise on the Pakistanis would be a major turnaround for the president-elect. In 2012, Trump took to his favorite social media platform, Twitter, to denounce Pakistan," the leading American newspaper said.
According to Pakistani account, Trump lavished extravagant praise upon Sharif and Pakistani people. "You have a very good reputation. You are a terrific guy," it goes. In addition, Pakistan is "a fantastic country, fantastic place" with the most "intelligent" people and "your country is amazing with tremendous opportunities".
Not satisfied with that, the account, commonly known as read-outs, culminates with this flourish: "Please convey to the Pakistani people that they are amazing and all Pakistanis I have known are exceptional people, said Mr Donald Trump."
"It is unclear to what extent these are direct quotes,but there was much bemusement both in mainstream and social media," the BBC commented.