The question you speak of is ontological. It's the field of psychological study where one contemplates reality, existence, and the sense of being. Your example 'how do we know that two persons see the exact same colour' is part of that. One could ask whether or not two humans experience softness in the same way, like petting a cat, it could feel entirely different to someone else than it does to you, but since you're unable to EVER convey what it's really like to you to someone else while using only words, you can never BE sure it's exactly the same sensation to the other person.
Take this one step further, and you're experiencing ontological doubt: when your senses are the only thing you can ever trust to provide an image of the real world outside, how can you be sure what you see or touch is actually there at all, or just your imagination? Does thinking something is real make it real?