(CNN) It's a case of he said, he said between two of the world's most powerful men.

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.

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 statement quoted President-elect Trump as telling Sharif "you are a terrific guy. You are doing amazing work which is visible in every way. I am looking forward to see you soon. As I am talking to you, Prime Minister, I feel I am talking to a person I have known for long."

The President-elect's office put out a statement saying the two sides "had a productive conversation about how the United States and Pakistan will have a strong working relationship in the future."

The Trump team did not answer inquiries from CNN asking whether the President-elect actually said what the Pakistanis claimed he had.

The danger

Readouts of phone calls between world leaders are usually summarized in order to protect leaders from incidental backlash -- like the one the Trump team put out.

They're dry and diplomatic statements recapping conversations using carefully chosen buzzwords.

And political insiders say the 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."

Sadanand Dhume, a scholar at the American Enterprise Institute, said that in India, "as in many parts of Asia, people are very unsettled by a sense of uncertainty" about the Trump presidency. But he added that policy makers in Delhi "are taking that phone call with Nawaz Sharif neither seriously or literally, so talk of this potentially derailing India US relations are premature."

"People are talking about that call," he said, "but basically it's a party joke. It's entertainment. It's unbelievable. No one doubts Trump really said it."

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The disconnect

In the past, the President-elect has been a vocal critic of Pakistan.

"Get it straight: Pakistan is not our friend," he tweeted in 2011.

Get it straight: Pakistan is not our friend. When our tremendous Navy SEALS took out Osama bin Laden, they did... (cont) http://t.co/s6u5o8Co — Donald J. Trump (@realDonaldTrump) December 6, 2011

"When will Pakistan apologize to us for providing safe sanctuary to Osama Bin Laden for 6 years?! Some 'ally,'" he tweeted in 2012.

When will Pakistan apologize to us for providing safe sanctuary to Osama Bin Laden for 6 years?! Some "ally." — Donald J. Trump (@realDonaldTrump) July 5, 2012

And Trump said in October if he was elected , the United States and India -- Pakistan's longtime adversary -- would be "best friends."

Speaking to reporters, a spokesman for India's Ministry of External Affairs said "we have only seen the one-sided version of that conversation."

Referring to Trump's apparent willingness to tackle "outstanding issues," he said that India believes the most pressing issue is "Pakistan's continued support of cross-border terrorism."

"To that extent we would welcome a dialogue between the US and Pakistan to resolve that issue," he added.

While the comments could have caused friction with Pakistan, they -- and the quotes the Pakistanis attribute to Trump -- fall in line with the President-elect's campaign pledge to employ the relationship-building skills he used in his business career in the diplomatic sphere.

It also could be another case of growing pains for a political newbie, if the quotes are accurate.

Some world leaders had trouble getting in touch with President-elect Trump immediately after his election

The President-elect is traditionally briefed by the State Department prior to making these calls. But Trump, as he's proven throughout his campaign, isn't one to stick to traditional political norms.

The State Department said it was contacted after the Trump team had already spoken with several world leaders.

"Quite frankly, nobody knows what the protocol is with Donald Trump," CNN Politics Executive Editor Mark Preston said.