PDI titles? Can you help me with this abbreviation?
The game is basically about telling your own story. In my experience it takes a bit of imagination to get enjoyment out of these kinds of titles (similar would be Birthright: The Gorgon's Alliance, or more recently: the Total War series) - Basically you conquer the world in one (or more) of several means. It is a grand strategy game.
(Oh! If you liked Birthright - The Gorgon's Alliance, it is worth checking out its spiritual successor on Steam, called: Sovereignty: Crown of Kings.)
So yes, a large overworld landmap, and battles that take part in a separate instance. You have ZERO control over battle instances. However, you influence battles ahead of time, as you get to choose commanders, troop formations, their orders, what spells they cast, etc. - So your decisions do greatly influence the outcome of each battle. Basically you issue orders and watch the battles play out.
The Dominions series gets updated all the time, and hence there have been four installments in this series (with an offshoot called Conquest of Elysium (1, 2, and 3), which is more of a rogue-like tile based version of the game).
The game series' graphics style is consistent and matches. Though it does look outdated. But what it lacks in graphic detail, it makes up for in depth and content detail. There are many different factions, which are different throughout three different era's. So you may get 20 different factions, that exist throughout three era's: meaning there are basically 60 different factions in the game, each with their own units and lore.