The difference is that nylon strings are made out of a type of plastic with the bass strings having wraps of metal. They are specifically for classical guitars.
Steel strings are used on "western" style guitars. Sometimes referred to as 'folk' guitars. These are popular for contemporary styles, pop, rock, blues, country,etc. They are brighter sounding. They do NOT sound better, just different.
They are NOT interchangeable. You CANNOT put steel strings on a guitar designed for nylon strings. It will cause severe damage to the instrument!