The fretboard is a thin, long strip of material, usually wood, containing frets that is laminated to the front of the neck of an instrument.

The fingerboard (also known as a fretboard on fretted instruments) is a part of most stringed instruments. It is a thin, long strip of material, usually wood, that is laminated to the front of the neck of an instrument. The strings run over the fingerboard, between the nut and bridge. To play such an instrument, a musician presses strings down to the fingerboard to change the vibrating length, changing the pitch. This is called stopping the strings.

(from Wikipedia)