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The color of a pixel in a document is represented as a set of numbers (for instance, 255, 0, 0 is bright red in the RGB system). From the document to the final display (screen or printer) those numbers pass through software and hardware layers which perform adjustments and corrections - those are the settings mentioned by Dave - resulting in different actual colors in different devices. That happens because neither eye/brain sensitivity nor physical/analog values scale linearly: changing the amount of ink or a LED's voltage by a factor of two won't produce a dot exactly twice as bright or dark.
But there's another point: the ranges of possible colors (gamut) of CRT, LCD screens and printers are different, and all are only subsets of the colors actually discernible by human eyes. In other words, many colors you'll see on screen can only be approximated, but never exactly reproduced on your 4-cartridge inkjet, and vice versa (those 7-plus colors photo cartridges help but don't eliminate the issue) no matter the settings.
Therefore, be aware that some discrepancies can't be avoided, due to physical limitations.
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