What a birthday calculator is measuring
A birthday calculator starts with the date of birth and a comparison date, then finds the next annual recurrence of that birthday on the calendar. From there it can calculate the number of whole days until the next birthday, the age reached on that date, and how much time has passed since the last birthday.
This makes it slightly different from a general age calculator. An age calculator is designed to measure total elapsed time between two dates, while a birthday calculator is usually a focused planning tool for the next milestone. For users searching how many days until my birthday, next birthday calculator, or how old will I be on my birthday, that narrower result is often the one they actually want.