The difference is a genetic one.
A dun isn't really a color, but more of amplifier (?). The horse will have a base color, bay (bay dun; this one looks like a buckskin), chestnut (red dun), black (grullo) even buckskin (dunskin) and palomino (dunalino), but will also be affected by the dun gene, so it will show certain characteristics (dorsal stripe, primitive markings)
A buckskin is simply a single dilute bay (carried one creme gene). Some will have "frosting" as well. Genetically they are EEAACrcr, EeAACrcr, EEAaCrcr.