Each scenario takes place on a dedicated map, and any progress made on this map will stay only on this map. Maps can range from a specific region, to the entire globe, and even to some new and unique geographies.
Movement around the map will also vary, as your armies must account for difficult terrain - such as forests and mountains, bodies of water and infrastructure upgrades. Unit speed will change according to the terrain, with some units being more capable in difficult terrain than others, and crossing large bodies of water, such as seas and oceans, will require embarkation onto transport ships.
In order to embark or disembark units, simply issue move orders that require the traversal of water. Your armies will organise themselves onto transport ships (which you may imagine as commandeered civilian ships, hastily-constructed transport barges or whatever suits your preferred aesthetic) and disembark at their destination. This takes some time, but does not require you to have ships in place already, as the army will provide their own.
Some units can be transported by air - so always check your unit cards and infrastructure upgrades to better understand how your armies can be moved.