So that's three different frets. All three are correct. One can be resolved by self medication or meditation, which ever you prefer. Bills discription is scroll work and the sawyer frets their way through the work. Dennis's discription is a thin kerf saw with a depth stop and looks like a gents dovetail saw. I'm sure someone smarter and more learned than I can add more to this.
I believe in the luthier craft, a fret saw is used to cut the neck of a guitar, mandion, ukelele or banjo in preparation for the cross bars, aka frets to be placed into. It is usually set to a specific width to accommodate the metal or hardwood fret bars used, making a tight fit.