Color and colour are different spellings of the same word. Color is the preferred spelling in American English, and colour is preferred in all other main varieties of English. The distinction extends to all derivatives of the word. Colored, coloring, colorer, colorful, and discolor are the U.S. spellings, and coloured, colouring, colourer, colourful, and discolour are preferred outside the U.S.
Both spellings are many centuries old. Color, now regarded as the American spelling, in fact predates the United States by several centuries. In early use the spellings vied for ascendancy with several other spellings. Colur, culoure, and coolor, for instance, were all in the mix before the modern British spelling gained permanent prevalence in the 17th century.1 The American preference for color took hold in the middle 19th century thanks in large part to the conscious simplification of English spellings by people such as the lexicographer Noah Webster.
Color, as used in the following examples, is the preferred spelling in the U.S.:
The “it” color of the moment is a visual pick-me-up. [Seattle Times]
They are very large and multicolored, often having two or three colors in different shades. [Auburn Citizen]
In some cases, OLED creates better color contrast and uses less power. [Wall Street Journal]
Though color occasionally appears outside the U.S., it is still considered a misspelling. Most non-U.S. publications favor the -our spelling used in these examples:
My daughter has impaired colour vision, mostly affecting the colour red. [Sydney Morning Herald]
Special decor touches of colour, texture and whimsy can bring heart-thumping feelings all year long. [Metro]
Woman returned shelter dog because its colour clashed with her curtains [Mirror]