What are the differences between a zero fret and a nut in terms of their functions and impact on the playability of a guitar?

A zero fret is a fret placed directly before the nut on a guitar, serving as the starting point for the strings. It helps to set the correct string height and can improve the playability by ensuring consistent tone and intonation. The nut, on the other hand, is located at the end of the fretboard and helps to space and hold the strings in place. It affects the playability by determining the string height and spacing, as well as contributing to the overall tone and sustain of the guitar.