If you would like to leave the transit area and pass the Schengen border (e.g. to visit the city), you will need a regular type C short-term Schengen visit visa.
You do not need an airport transit visa to transfer through an Italian airport as an Indian citizen (in any case, your valid US visa would exempt you from any Schengen airport transit visa requirement), as long as you stay in the international (non-Schengen) transit area of the airport.
An airport transit visa, even if applicable, does not allow you to leave the international transit area of the airport. You will not be permitted to enter the Schengen area without exceptional circumstances (e.g. cancelled flight).
An airport transit visa (ATV) authorises you to pass through the international transit
zone at an airport located on the territory of the Schengen State and to await a
connecting flight to a non-Schengen country. The ATV does not allow you to enter the
Schengen territory (to stay at a hotel or to take an onwards flight to another Schengen
State, for example).