Why does \color{blue} differ from \color{Blue}?

Because that's how the colours are defined :)

Colour names are case sensitive, and red, green, blue are the ‘standard’ (1,0,0), (0,1,0), (0,0,1) RGB colours respectively.

In section 4 of the xcolor manual (pg. 38 for v2.11) the list of other colour names is given; under the dvipsnames section you can see that there are many more colours defined with initial-uppercase names. Personally, I find those Red, Blue, and (especially) Green colours to be much more attractive as they are a little more muted.

A natural color is defined by its wavelength. If you want to print it you have to convert it into a color model which allows the mixing of base colors into the needed color. Such color models are very different and a blue in model A is often different to a blue in model B.

"blue" is a rgb color and "Blue" is defined as a cmyk color and handled by a different driver for your output. If you want to be sure, that you use the same driver, then specify one:

\documentclass[dvipsnames]{article}


\usepackage[rgb]{xcolor}

\begin{document}

{\color{Blue}\bf Blue} versus {\color{blue}\bf blue}.

\end{document}

instead of [rgb] you can also use [cmyk]