Fairymount is the name of the townland- in the civil parish of Kilgefin.
Roman Catholic registers for that period often used a Latin form of the names (such as Patritius for Patrick, Maria for Mary, etc.).
A baptismal record is a record of a church cerremony while a birth certificate is a civil registration of a birth.
I'm not familiar with that area of Roscommon but Kilbride (on the baptism) might be the name of the Catholic parish and Ballyleague on the birth certificate the registration sub-district (the registration district is Roscommon).