Yes sure, it is valid within Italy too. All trains run by Trenitalia, the state operator, are included. Trenord, TILO too, etc.

.italo high-speed trains are not included but there are always Trenitalia trains on the same route (even more frequently).

Which journey are you looking at (+ which date)? Feel free to add a screenshot. We'll be able to help with that.

The pass is not valid on buses, subways, trams in cities. These shouldn't appear in the planner anyway.

Thanks for response

We have planned florence, Rome and Vatican .

For internal local travel within Rome or florence we did not see trains which we did not find stations we are looking for like Pantheon 

Understood Italy seperate pass is valid for all public transport in and within Italy.

However this not valid again for other EU cities 

Eurail is not valid on buses, trams, metros.

It is valid on many suburban rail networks but in most cities these are of limited use for the average tourist.

A local day ticket for cities valid for most/all public transport will be cheaper than a Eurail pass day so plan only to use Eurail on days you are making longer journeys.