Two people are born at the same moment, but they don't have the same birthdays. How could this be?

Common Wrong Answers
“They are twins.”
While twins are often born at the same moment, they would still share the same birthday. The riddle implies that they have different birthdays despite being born at the same time.
“They were born on a leap day.”
Being born on a leap day would mean they share the same birthday every four years, not different birthdays. The riddle suggests a scenario where their birthdays differ.
“They are born in different years.”
If they are born in different years, they would not be born at the same moment, which directly contradicts the premise of the riddle.
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