In antiquity and exploration there is only one type of shipIt could depend on the Age.
As posted, modern capital ships are usually too big for most rivers, either by depth or maneuverability: a 240 - 300 meter long hull does not maneuver around river bends well, and a 10 - 12 meter minimum draft is too deep for many rivers, or many parts of rivers.
But prior to the Modern Age, ships were dramatically smaller. The largest ship of the line in the Royal Navy in the 18th century was less than 70 meters long and the Vikings regularly traveled up and down almost every river in Russia with their long or round ships, portaging between rivers on log rollers when necessary.
IF the game wanted to go into that much detail, rivers could be navigable by all warships in Antiquity and Exploration, only the smaller ships (non-Battleships or Aircrfaft Carriers) in Modern Age.
Personally, I think that's more detail than we need, but the option would be fairly easy to add, I suspect.
Only in Modern do you get Heavy and Light ships