The classical guitar has nylon strings and a wider neck than the 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.
The steel string acoustic has steel strings and is good for strumming, picking or fingerpicking. This is the type of acoustic guitar you will hear in most modern styles of music e.g., Acoustic Rock, Pop, Folk, Country, and Blues.