No. 256 colors = 8 bits * 3 colors = 24 bits. So 24 or 32 bit color has 256 shades of each.
16 bit color VARIES depending on mode. Popular representations are 5-5-5 (where each is 5 bits or 32 gradations) but 5-6-5 is also widely used (there are 32 gradations for red and blue, and 64 for green).
