The classical guitar has nylon strings and a wider neck than other types of guitar. It is most commonly used for playing Classical, Flamenco and Fingerstyles. Generally it is much cheaper than other types of guitar and is recommended for beginning guitarists.
The steel string acoustic has steel strings and is most commonly played by strumming or fingerpicking groups of notes called chords. This is the type of acoustic guitar you will hear in most modern styles of music e.g., Acoustic Rock, Pop, Folk, Country, Blues and World music.
Acoustic guitars can be amplified by placing a microphone near the sound hole or by placing a portable pick-up on the body of the guitar. This is common for performances at large venues where the acoustic guitar needs amplification to be heard.