No people dont see the same thing when they see colours (I will stick to the UK English Spelling).
This is shown up in Colour Blindness, I am Colour Blind in the Turquoise area (Blue/Green). Its not that I cannot see anything that is Turquoise in Colour, but unlike people who claim that it is an individual colour all I see is a shade of Blue or Green not a mix of both.
So what I see as one colour, the majority of people see as another.
This is not a problem with my eyes (since they can see the turquoiuse frequency of light), but more of a question of recognition that this frequency is in fact a distinct colour.
Heres an Experiment to prove my point.
Gather a dozen people together at sunset and ask them what Colour it is.
I believe that the majority if pressed will not be able to give a precise answer that is the same as their neighbours.