Bill Gates, the billionaire entrepreneur and philanthropist, has claimed Donald Trump twice asked him the difference between HIV and HPV and knew a “scary” amount about Gates’s daughter’s looks.

The remarks were recorded at a recent Bill & Melinda Gates Foundation meeting, where Gates took questions from staff, according to MSNBC’s All in with Chris Hayes show, which broadcast the footage on Thursday.

Gates told the audience how Trump had encountered his daughter Jennifer, now 22, at a horse show in Florida. “And then about 20 minutes later he flew in on a helicopter to the same place,” the Microsoft co-founder said. “So clearly he had been driven away but he wanted to make a grand entrance in a helicopter.”

Gates himself met Trump for the first time in New York in December 2016, he recalled: “So when I first talked to him it was actually kind of scary how much he knew about my daughter’s appearance. Melinda [Gates’s wife] didn’t like that too well.”

Exclusive footage obtained by All In... Bill Gates dishes on his meetings with Donald Trump. More tonight at 8PM ET. #inners pic.twitter.com/Zoehj1WTfk — All In w/Chris Hayes (@allinwithchris) May 17, 2018

They met again in March last year at the White House. Gates continued: “In both of those two meetings, he asked me if vaccines weren’t a bad thing because he was considering a commission to look into ill-effects of vaccines and somebody – I think it was Robert Kennedy Jr – was advising him that vaccines were causing bad things. And I said no, that’s a dead end, that would be a bad thing, don’t do that.

“Both times he wanted to know if there was a difference between HIV and HPV so I was able to explain that those are rarely confused with each other.”

Trump since appears to have abandoned plans to investigate debunked theories linking childhood immunisations and autism. Robert F Kennedy Jr told the Guardian earlier this year that parents and children’s health advocates felt “enormous betrayal and disappointment” at the decision.

The UK’s National Health Service website lists “What’s the difference between HPV and HIV?” as one of its common health questions. It says: “Human papilloma virus (HPV) affects the skin and moist membranes. HPV can cause problems such as verrucas, genital warts and abnormal cell changes in the cervix.

“Human immunodeficiency virus (HIV) attacks the immune system. HIV infection can lead to Aids; however, with early diagnosis and treatment, most people don’t go on to develop Aids.”

Gates is hardly known for his comic timing but he frequently prompted laughter from the audience at the foundation event. In one anecdote he said: “When I walked in, his first sentence kind of threw me off. He said: ‘Trump hears that you don’t like what Trump is doing.’ And I thought, ‘Wow, but you’re Trump.’ I didn’t know the third-party form was always expected. ‘Gates says that Gates knows that you’re not doing things right.’”

Trump has a now-familiar verbal tic of referring to himself in the third person.

Hayes said his show had sought comment from the Gates Foundation but has not yet received a response. Tara Dowdell, Democratic strategist, told the MSNBC host: “We’re looking at a president that doesn’t know the difference between HIV and HPV but he has memorised Bill Gates’ daughter’s appearance.

“So if he spent more time actually learning policy, if he devoted just a quarter of the time that he devotes to harassing women and gawking at women to actual policy, memorising and learning policy, I think the country would be a lot better off.”