The main difference between a piano (a standard acoustic piano) and a digital piano is the mechanism that produces the sound.The acoustic piano produces sounds by channeling the power of the fingers pressing the keys into the hammers, which strike the strings. The vibrations produced by striking the strings are transmitted to the soundboard, and diffused richly, which amplifies the sound. 

Digital pianos are equipped with hammers, though. These are not for the purpose of striking the strings, as with an acoustic piano, but instead are employed to capture the dynamics with which the key is played, yielding a dynamic response to touch that more closely approximates the experience of playing an acoustic piano. Digital Pianos as the name says run by power supply.

What do people prefer and why ?

To explain in one line digital pianos produces good sound with low maintenance whereas acoustic piano produces more natural sound but need regular maintenance