Italy has an official ID. ID is Identity Document. The Carta d’identità. While generally a driver's license contains most information of an ID and does qualify to prove who you are (can serve to identify), it is not an ID, neither in Italy (as Italian Wikipedia tells me), nor in the EU. It does lack some information required to make it a proper ID.
The prevailing purpose of a driver's licence is to document which types of motor vehicles you are allowed to drive.
It is not an identification document (no citizenship entry for one thing).
It can sometimes be accepted as such, depending on the situation, but do not assume that will always be the case.
For the crossing of internal Schengen borders, a driver'...