Does 'sore' really convey that idea that some part of the body has been sore for some time? I don't think "I have a sore throat" proves that theory, does it?When you say "I have a sore foot." it conveys the idea that the foot has been sore for some time. "My foot hurts." means your foot is sore right now.
So does 'sore' generally refer to the parts of the body like legs, arms etc that we can move by means of muscles or joints? Things like the brain, liver, spleen can't be sore then, right?When something is sore, it generally hurts (or hurts more) whenever you use or touch it. In other words, it is sore even when it doesn't hurt right now, therefore "soreness" is a thing that has duration. Your sore throat hurts when you swallow. Your sore foot hurts when you put weight on it. Etc.