The main difference between a piano (a standard acoustic piano) and a digital piano is the mechanism that produces the sound.
The 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. When these vibrations combine with the resonances of strings other than the ones that were struck, it creates a unique sound.
In contrast, the digital piano has no strings. Each key is a switch to produce a specific sound, so to speak. An electronic tone generator produces the sounds, which are amplified using a speaker.