These are similar, but the Kuiper Belt is bigger and farther from the sun.
The Asteroid Belt is between Mars and Jupiter. The Kuiper Belt is from the end of the planets' orbit to about 55 astronomical units from the sun. That's about 20 times as wide as the Asteroid Belt.
So, they are both areas of space with lots of asteroids, but the Kuiper Belt is bigger and farther away from the Sun and the Earth.
Asteroid Belt is located between the orbits of the planets Jupiter and Mars. It is made up of thousands small objects. Since these objects are too small, they are not considered planets. Though, a few of them, like Ida, have their own moons.
Kuiper Belt is located beyond the orbit of planet Pluto. Kuiper Belt is also made up of millions of objects too small to be considered planets. Some of them, like Pluto, are large enough. Since they are large and their gravity is bigge, they became spherically.
The composition of these objects is frozen gas with small amounts of dust and we know them by the name of comets.