What you SEE, and What you DON'T
So many times we glance over an image, presume what we expect to see, and do not give it a second thought. We look and almost mindlessly allow our brains to compute the possibilities of visual representations, and by a calculation of random colors, chance, and circumstance, our mind perceives what is considerable to us as reality, deducted of course by reason.
This is the exact reason that the philosophers of old considered it to be one of the paramount virtues needed to create epistemology, that is to say the study of the nature of knowledge.
What reason then, is there for two people having looked at, or experienced the exact same thing, can perceive the event completely different? How can one reconcile the idea of reality, as a constant thing, with the fact that indeed each individual seemingly experienced their very own reality? Is it true then to assume that there are multiple realities then? Can we say that my reality is different than yours? How then can we have right and wrong? What is right for me, might not be to you?
All-in-all I think it is a vast question with myriad possibilities to branch off and into. I can be said that each mind is in fact a different world, however one imagines this concept as a metaphor, not an alternate reality. In Einstein's theory of relativity there does exist a branch of physics, called "String Theory", that deals with theory in terms of the existence of what they term as a "Multiverse", which by definition implies that there are multiple, and simultaneous, universes (dimensions) that exist all at once, in the same space and time. So things can get very complicated, very fast... (see video below for a mind blowing quick intro into string theory).
How can people conceive of completely different experiences, through the same event? I have witnessed this phenomenon, as I am sure you have too. I bet in your case the color of an object or clothing seemed one color to you, and another to the other person. Or was it the time of day, the weather, the sounds involved, or the voices heard? So many things can be mis-interpreted or over-interpreted and different outcomes arise.