I think you'd be best served by calling Jason at Zoli USA or a dealer like Rob Carlson. Go to the Zoli Italia site and download the catalog and see the references to most of the versions and their differences.
Different configurations have been offered over the years so there's not really an always-true definition. The primary differences are really only between the game/Expedition, Pernice and sporting.
The Pernice is a newer field gun offering and the differences are rather obvious.
Expedition is the term used for the other game gun but is sometimes called in advertising as the "Expediiton game gun." I'm otherwise not aware of any distinction. The Expedition has typical field stock/barrel differences. Compared to the sporting, it has a smaller forearm, usually a narrower stock, grip is Woodward or Prince of Wales, a field slope from comb to heel, and, a wood or smaller butt pad. The forearm and stock are therefore lighter to reduce overall weight. The barrel has a very narrow rib at about 5mm. Flat rib only. Different filing pattern. May or may not have a mid bead.
The action is the same as the sporting version. The trigger of the Expedition and Sporting/Kronos are the same except it may or may not be TiN coated. Sometimes, but not always, the Kronos trigger isn't TiN coated. The same trigger is used in both the 12 and 20 gauges (Zoli only has two receiver sizes). In fact, the double trigger used in the rifles will also fit in the shotgun with Norbert making some tweaks to eliminate inertia block and making the safety just be a safety.
The Ambassador, Lusso, Extra, Anniversary, Columbus, Dakota, etc. are wood grade and engraving differences only. The Expedition and sporting have had different engraving over the years. Mid rib on the Expedition may be solid or vented.
If the majority of the shooting is going to be at clays, you really need to go that way. The lighter weight, steeper drop from comb to heel (more cheek slap), thinner wood (sharper cheek slap), and grip style will all combine to make the game version be less pleasant in terms of felt recoil.
Just to point out that there is no always-true, my primary hunting gun is a 20 gauge Expedition but it has a pistol grip stock but otherwise field dimensions.
All the above may be wrong. So, ask Jason or Rob. Just do not get into why the extended chokes on the sporting versions have different color bands from one gun to the next.
. . . more than you asked but there it is. Misinformation is free.