Two clues that indicate if a guitar is made for steel or nylon strings:
The headstock is usually slotted with white plastic (these days) rollers.
The bridge will have tied on strings:
The main difference, although not easily visible, is that a nylon string guitar is often fan braced, a lighter bracing not meant to stand up to the tension of steel strings and light enough to allow the nylon strings to ring.
Putting steel strings on a nylon string guitar endangers the guitar, which was not meant for the extra tension.
Putting nylon strings on a steel string guitar won't pull the guitar apart, but the guitar is built for higher tension strings to get the best sound, so it's not advisable.
Nylon string guitars are common in classical music, flamenco music, and South American music. Many finger-pickers, like Chet Atkins, Duck Baker and Jerry Reed make/made use of nylon string guitars for effect. Willie Nelson likes the sound he gets from his nylon string guitar, Trigger.