Is there a term for somebody two people who aren't related who were born on the same day of the same year Or just for two people who share the same birthday regardless of the year?

No, there are 6 billion people in the world. So the chances of two people being born on the same day are extremely likely. But there is no Word for it. It's just, well, not even a covincidence because it's so likely.

With 6 billion people in the world, and only 365 days in the year, on average there are more than 16 million people who were born on any particular day.