Comparing wig shades under stage lights

My new identification photo makes my natural brown hair look distinctly reddish, although I have not dyed it. It looks different in my usual mirror. Previous daylight pictures look less red. I am trying to work out whether the difference comes from the light, the camera, or the printed photograph. I found hair color analysis while searching for better language to describe what I see. I am only trying to describe my existing color. A small controlled comparison seems more useful than a transformation. Would you take a fresh picture beside a neutral background and compare it with an unedited daylight image? I would leave filters off in both cases. The framing could stay similar too. The print is the part I find hardest to explain. What would you check first? I would like to know whether a retake is worth requesting before assuming my everyday view of my hair is wrong.