There isn’t a size between elongated and round, but there are many different styles of toilet seats to choose from. You can get D-shaped seats that are mostly European. These fit concealed tank toilets and wall-hung models because they are sleek and very modern in design.
You can also get open or U-shaped seats that have the front section cut away. These are great for hygiene because you don’t get splashes and drips trapped under the seat rim. For this reason, you are more likely to see U-shaped seats in public toilets.