There are many different racing karts around. In America and all over the world. They each have their own styles and ways they are used. I will generalize a little bit here and then explain further on each page.
Speedway Kart on a Pavement Oval
The Speedway Kart is seen mostly in America and races primarily on pavement oval(left turn only) tracks that are between a 1/6 of a mile and 1/4 of a mile long.
Some people like to race on dirt. The Dirt Kart is their easy choice. All dirt tracks are oval, and this kart is very similar to the speedway kart.
Champ Kart on a Pavement Oval
The Champ Kart is the type of kart with a roll cage on top. This offers added protection onto an already safe form of racing. Plus some people just think it looks cooler to race one of these.
Shifter Kart on Sprint Track
The Shifter Kart is the kart that has a gearbox for shifting through gears. These are very fast and exciting. Most professional kart racers race these types of karts.
The Superkart The superkart is the fastest type of kart in the world.
The Rotax Kart is one of the most standardized karts in the world right now. This is very popular as everything is as close to a standard as possible and it really allows the drivers skill to be shown.
Remember that the different Kart types are regional sometimes and you may not see some of these near where you live. Look around for local kart clubs or tracks to see what they are racing!