However, they've started the habit of creating new paint names for each new box, leading to a really silly proliferation of the same paints under different color names. They published a conversion chart, but here's a cleaner version in case that one disappears from the internets.
In all cases, the format is [SoB Paint Set] = [Standard AP Color]
FFP0703 - Heroes of the Old West Paint Set
- Shadow Black = Matt Black
- Spirit White = Matt White
- Light Flesh = Barbarian Flesh
- Dark Flesh = Oak Brown
- Saloon Red = Dragon Red
- Portal Blue = Deep Blue
- Desert Yellow = Desert Yellow
- Loot Gold = Greedy Gold
- Pistol Metal = Gun Metal
- Soft Tone Ink = Soft Tone Ink
FFP0704 - Creatures of the Void Paint Set
- Fang Bone = Skeleton Bone
- Leather Brown = Leather Brown
- Cynder Yellow = Daemonic Yellow
- Molten Orange = Lava Orange
- Crimson Hand Red = Chaotic Red
- Serpent Skin = Greenskin
- Jargono Green = Angel Green
- Tentacle Blue = NO TRANSLATION (Unique to set)
- Dark Stone Purple = NO TRANSLATION (Unique to set)
- Dark Tone Ink = Dark Tone Ink
We also own the Super Dungeon Explore paint pack, and although ArmyPainter has not published a cross reference yet, I'll try to figure out a reasonable way to format the list here.