whereas 8-bit uses 4 colours (including transparancy) in an 16x16 (I think, please correct me if I'm wrong) radius.
8-bit is such a non-specific term ... lots of systems with 8-bit cores used entirely different graphical limitations ,
compare the limits of the ZX Spectrum with the GameGear for example

Nowadays 8-bit seems to be a term for NES though ,
so in that case it might only utilize a set of 4 BG palettes , each consisting of 4 colors , but the last is always transparency.
The palette might be changed between 16x16 blocks of pixels , meaning that each 2x2 tile section must share the same palette.(so only 3 useable colors per 16x16 block)
But from what I've heard (haven't worked with NES much) it also uses a "BG color" , which is visible through the transparency , correct?
As far as sprites go , there's 3 useable colors per sprite , and the sprites uses 4 separate palettes (not necessarily the same as the BG palettes).