A number of differences exist between electric and acoustic guitar strings, and they're easy to spot. Strings are designed with the instrument's particular properties in mind, and one string type should never be substituted for another.
Electric Guitar Strings
Electric guitar stings consist of steel wire. The wound strings, used for the three lower bass strings, are steel cores wound with steel or another similar alloy.
Acoustic Guitar Strings
Acoustic guitar strings are also made from steel wire, but the lower bass strings are wound in bronze alloy. Bronze is used for its resonant acoustic qualities, and is louder on an acoustic guitar than steel.
Nylon Acoustic Guitar Strings
Nylon acoustic guitar strings, also called classical guitar strings, do not use metal cores at all. The top three strings are made from nylon or polymer, and the bottom three strings consist of a stranded nylon or polymer core, wound with silver or alloy.
The metal in electric guitar strings is chosen for its superior magnetic properties, in order for the guitar's electromagnetic pickup to reproduce sound. Standard acoustic strings have similar magnetic properties, but the metal used is optimized for acoustic sound. Nylon strings have no magnetic properties. Acoustic guitars are usually amplified by piezoelectric pickups, which operate on vibrations rather than magnetics.
Although no damage will occur to a steel stringed acoustic guitar if electric strings are swapped for acoustic steel strings, or vice versa, the sound produced will be compromised. Steel strings must never be used on a guitar designed for classical strings, as the increased tension will severely damage the instrument.