Asteroids

Asteroids are rocky and metallic objects that orbit the Sun but are too small to be considered planets. They are known as minor planets. Asteroids range in size from Ceres (The largest and the 1st one to be found) which has a diameter of about 1000 km, down to the size of pebbles. They have been found inside Earth's orbit to beyond Saturn's orbit. Most, however, are contained within a main belt that exists between the orbits of Mars and Jupiter. Some have orbits that cross Earth's path and some have even hit the Earth in times past.
Asteroids are material left over from the formation of the solar system. One of the theory yet presented suggests that they are the remains of a planet that was destroyed in a massive collision long ago. More likely, asteroids are material that never merged into a planet. In fact, if the estimated total mass of all asteroids was gathered into a single object, the object would be less than 1,500 kilometers (932 miles) across i.e. less than half the diameter of Moon.

Meteorites

The definition of a meteoroid is a solid object moving in interplanetary space, of a size considerably smaller than an asteroid and considerably larger than an atom.
Meteorites are solid extraterrestrial material that survived passage through the Earth's atmosphere and landed on Earth. It is believed that most meteorites are probably fragments from the asteroid belt that lies between Mars and Jupiter. A small number of rare meteorites are fragments of the Moon and Mars.

Types of Meteorites:
There are three major types of meteorites: stoney, stoney iron, and iron. More that 90 percent of all meteorites are the stoney type, which are made up mostly of silicate minerals.
Furthermore Stone meteorites consist of two groups i.e. chondrites and achondrites.
Most chondrites have remained unchanged since their formation 4.56 billion years ago, shortly after the formation of the Sun. Almost all chondrites contain chondrules - small, gaseous, spherical inclusions that formed during the solar nebula.
Achondrites appear to have been chondritic before being altered by a heating or impact event. These meteorites are much rarer than chondrites.