Two people were born on the same day, same year, and share the same birthday.
One is 2 years old, the other is only a few days old.
What's going on here?
They were born on
the New Year's Eve (not necessarily of the western variety), and one of the families is using the East Asian way to measure age.
Apply some other bit of science, assuming they were born at the same time,
.. but on Mercury.
According to Mercury's Wikipedia entry, Mercury rotates extremely slowly, so
An observer on Mercury would therefore see only one day every two years.
The two people are the same age, they are both two years old, which on Mercury is equal to very few (one, to be precise) days.
This could be an historical question
The change from the Julian calendar to the Gregorian calendar didn't happen at the same time in every country. If one person was born on February 29th in a country that was still under the Julian calendar, and the other was born on the same day in a country that was now on the Gregorian calendar, then one would have a birthday every year, while the other had one every four years, despite being born on the same day.
It's all about space and time!
They were born at same time but not in the same planet. Suppose that both were born at their respective planets at the same universal time (which on Earth would be, for example, March, 22th 1988).
But at the moment of answering this question both planets had completed different translations around their star. So if person A is at Earch he/she is now 30 years old, and if person B is at a planet which translation time is a little slower (so the planet have completed only 28 laps around it's star, rather than 30) he/she will have only the age of 28.