Buckskin: Black + agouti + cream.
Dun (bay dun, anyway): Black + agouti + dun.
Both dun and cream are dilution genes, which is the reason bay dun and buckskin look so similar. Dun dilutes the body color, leaving the normal color on the head and legs. In addition, it adds markings specific to the gene such as a distinct dorsal stripe, shoulder barring, and leg barring. Dun is also a complete dominant, meaning it will cause the same effect regardless of whether the horse is heterozygous or homozygous.
Cream is the dilution gene responsible for turning bay into buckskin, chestnut into palomino, and black into smoky black. Cream, however, is an incomplete dominant, meaning heterozygous will cause a certain amount of dilution, but homozygous will cause further dilution. Turning buckskin to perlino, palomino to cremello, and smoky black to smoky cream.
Dun can also affect any color. You can have a dunkskin (buckskin with dun), bay dun roan, grullo, etc.
Buckskin can and do have pseudo dorsal stripes called countershading that are not caused by dun. Bay duns are also typically a flatter, duller color than buckskin which are usually have a much golder tint to their coat. Oooor if you end up with a horse with the much more gold coat, but has the listed dun markings, it's probably a dunskin (example: Hollywood Dun It).
Whew. I think that's about as best as I can describe it.