Birthday - the Birthday segment attribute helps to create a segment of those users who have birthdays updated/not updated in their profiles.
Has Birthday - Filters for guests based on the date of their birth anniversaries i.e. depending upon the operator and value selected, the attribute includes all the guests who have their Birthday's in that specified time duration.
For instance, in this segment, all those users will be included who have their birthday in the current month i.e. April (starting from April 01- April 30).
Birth Date - Depending upon the operator and value selected, the attribute includes all the guests who have their Birthday till date (i.e. the date segment is created) in the specified duration.
For instance, in this segment, all those users will be included who have their birthday in the current month i.e. April (starting from April 01- April 15). Just to be clear, it will include the guests from the current month starting date till the date segment was created and here segment was created on April 15.