If the word Sushi is used alone, it usually refers to Nigiri Sushi, which is the main type of sushi served in Tokyo.  Most variations of this use fish or seafood in some way.  This is mostly because Tokyo is full of seafood of all kinds.  This kind of sushi is usually made by hand.

            Oshi Sushi, which means pressed sushi was invented by rice merchants of Osaka, which is the financial capitol of Japan.  They take vinegar rice, pack it into a mold, and cover it with marinated fish or other spices and ingredients.  They wait a little while, and, when they take apart the mold, they have a loaf of sushi that can be cut into smaller pieces.

            Chirashi Sushi means Scattered Sushi.  It is the easiest type to make, and is made in almost every Japanese kitchen.  It is simply rice with other tasty things mixed in.  Many times, Japanese children will take this to school for lunch.

            Maki Sushi is also known as Rolled Sushi.  It is usually made of thin strips of various ingredients put on a bed of vinegar rice and then put on a sheet of seaweed, or Nori.  This is usually called Nori-Maki Sushi.  It is the most common type of Sushi in the U.S.  Almost everything can be rolled into a piece of Nor-Maki Sushi.

            Maze Sushi is also known as Mixed Sushi.  A lot of various kinds of Sushi fall into this category.  Inari Sushi, a kind of Maze Sushi, is made of fried bean curd stuffed with vinegar rice.  Fukusa sushi, also known as silk-square sushi, is made of square, thin omelets that are wrapped around vinegar rice.

            As you can see, there are many different types of sushi, even more than are mentioned in this paper.  Sushi is now an art form of sorts.