The first one is a birth act, the second one is a birth certificate
The birth act it is written by the registrar when someone goes to declare the birth of a child.
The second one is a legal paper that "certificate" what it is written on the birth act.
The second one is useful to request the italian citizienship, not the first one.
The first one has more details,like name of kid, father's name,age and job, mother's name and age, address where the baby was born, and sometimes name of the lady (obstetrician) who helped the mother to give a birth of baby