This query will return the records with a birthday date of 9pm on 20th January 1990, pretty specific. Check whether your birthday field is storing the time component of the datetime values
Assumes time component and it will be defaulted to 00:00:00.000 so you get all the 20th records
SELECT * FROM student WHERE birthday BETWEEN '1990-01-20' AND '1990-01-21'
This drops the time component from the comparison
SELECT * FROM student WHERE CONVERT(DATE,birthday) = '1990-01-20'