Seems some people can't separate style from technology.
In the RGB colorspace, you have:
8 bit graphics means no more than 256 colors, because 2^8 = 256 (or "Hundreds of Colors")
The NES only used something like 16 or 24 colors at a time, and even the Sega Genesis only used about 256 colors at a time. Exile and Realmz both utilize 8-bit graphics, as does DOOM and even Quake I.
16 bit graphics: 2^16 = 65536 different colors (or "Thousands of Colors")
The SNES system allows for a most of these colors to be used simultaneously, yet most games opted not to. During the SNES era, most graphics were still illustrated as opposed to rendered, so the color palette was kept small for simplicity's sake. Most graphics used an "outline," typically black, to distinguish the sprite from the background.
Fallout on the Mac uses 16-bit graphics, which I presume were rendered in 24 bit and dithered to 16 bit. Avernum also uses 16-bit graphics.
24 bit graphics: 2^16 = 16.7 million colors (or "Millions of Colors")
Unless one is dealing with a snobbish photographer, graphics don't have more colors than this.
32 bit graphics: 16.7 million colors PLUS 256 shades of transparency
Transparency allows you to position graphics over one another without ugly aliasing or without using an outline. This would allow you to simulate glass, translucent water, fog, smoke, or supernatural things like a ghost. When you use layer transparency in Photoshop, when you render something from a 3D program with an Alpha channel, you are using 32-bit graphics.
I believe Unreal uses 16-bit color with 8 bits of transparency.
STYLISTICALLY, many SNES games, including Final Fantasy III/VI, Mario World, Yoshi's Island, etc, are closer to the 8-bit graphics used in games like Realmz and Exile. It wasn't until later games, like Super Mario RPG, that developers started really showing off the technology of the SNES. Most game graphics from consoles in this era were illustrated, and thus had a limited color palette.
Once machines like the PSX and the N64 came out, everybody just started using rendered graphics (as opposed to illustrated) which are typically very rich in color.
Basically, it boils down to either drawing your graphics pixel-by-pixel (illustrated), or learning an arcane 3D program and rendering each of your sprites (rendered).
Hope I cleared up some confusion about color...
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