But the fact that color illusions work the same way on most people indicates that most people probably do in fact experience color the same way. If you mix tiny red dots and yellow dots, everyone who can see colors will see orange, even though no orange dots exist.
However, as has been mentioned above, some people have visual receptors that react differently. I can see green and red easily, but when they give those “what number do you see” color perception tests with the little dots, I often don’t see any obvious numbers. So it seems that when red light stimulates my retina and sends a message to my optic nerve, I’m not getting the same message to my brain that most other people get. Which means I probably when “red” or “green” gets to my brain I’m not seeing the same red or green that most people see, even though I can see red and green.
Since you’re talking about the actual experiences of the same wavelength mixture, not whether people are capable are usually distinguishing between different wavelength mixtures, I don’t think we can really tell, but my guess is that those experiences differ more than you might naively expect.
Anyway, you’re not taking this far enough. We don’t know that people experience a square on a piece of paper the same way, or a face, or sounds, or temperature, or any other kind of sensation, but the more complex the input, I would assume the broader the differences in experience.
We get information via our senses, and we can measure certain aspects about those organs, and we can measure a bit of what regions of the nervous system are active when we do so, but at no point in those measurements are humans all alike, and a lot of it changes with age too. For example, there’s a study somewhere that seems to indicate that young people (up till the end of puberty, in fact) have a really hard time differentiating between angry faces and scared faces.
The answer is a definite no, as others have already pointed out in the case of well known color blindness and with the existence of various mutant color pigments in the retina. More interesting is that some women are tetrachromats and studies have suggested that anywhere from 2% to 50% of women may be tetrachromats. This is because there are color pigments on the X chromosome. If a woman’s X chromosomes are carrying different mutants, some of her cones cells will express one and some the other due to the phenomenon of X-inactivation (one of the X chromosomes is always turned off). So if you think your wife has strange color vision, it may be because she sees a much richer set of colors than you do.