I am a high school student interested in astronomy and physics, and I am trying to understand the difference between color temperature and effective temperature of a star. As I have searched this forum, I noticed that this question has been asked before, but I have yet to find a clear and comprehensive answer. Can someone please explain the distinction between these two concepts, and how they relate to the study of stars? Additionally, I would like to know which of the two temperature measures is considered more precise in the field of astronomy.
Color temperature refers to the temperature of the star if we fitted a blackbody curve to only measurements of its visible light spectrum (i.e. the $400 - 700$ nm range).
However, if we gathered data about much shorter wavelengths of EM radiation (like UV) from that same star, we could in theory find that it deviates from our already fitted blackbody curve for visible light. For example, this challenges our assumptions of the photosphere's physics - there could be some degree of absorption in the photosphere that we didn't anticipate.
If we then try a better blackbody fit against both the UV and the visible wavelength measurements, we can estimate what the "effective" temperature of the star actually is (which provides a better estimate of the "actual" temperature of the star)