This story has info about how passengers were turned away from boarding their flights. Some of them had had the type of tests that WERE on the airlines list.
www.independent.co.uk/travel/news-and-advice/covid-test-uk-flight-quarantine-heathrow-chicago-b1788742.html
My school were recently trying to book a flight to China for one of our students. He had to have a specific type of antigen test (there is more than one type). The type of test he needs to be able to enter China is not widely available. Even a doctor in the bigger hospital in the area didn't know where it would be available.
It seems there is so much variety in testing that there is no gold standard, which is available, and is standardised between countries. Very hard for passengers.
Brussels police ordered to attend a right wing conference attended by Braverman and Farage