Actually it's even more complicated than I outlined ;)
For example, the following could all result in different looking images:
Computer a + video card a + monitor a
Computer a + video card b + monitor a
Computer a + video card a + monitor b
Or any mixture of the above.
Or even:
Computer a + video card a + monitor a + software package a
Computer a + video card a + monitor a + software package b
Even the type of connector seems to alter things - I've just had a new PC and I'm running two screen both off DVI-D outputs. Before that I ran one monitor off DVI-D and one off a standard VGA cable and despite the fact the monitors are identical the colours were different. Now they're running off one card with the same connectors the colours are the same!
And that's even before people start changing their colour profiles within either their photo editing software and/or their system setup ;)
It's all good fun 🙂
my orders are to sit here and watch the world go by