Asteroids are celestial bodies that vary in size and may contain elements. Even though an asteroid can be rather large, none have been seen close to planet-size. Asteroids are not always present in a solar system, but when they are found, there can be very few of them, or there can be so many that it makes a large asteroid field. When destroyed, Asteroids can drop Iron.
Asteroid Field vs Asteroid Belt
Any grouping of asteroids is called an asteroid field, no matter the number. The asteroid belt is only a description of a particular type of grouping; it describes a grouping that encircles a planet, creating a belt.