Intensive exercise causes Delayed Onset Muscle Soreness (DOMS), which peaks between 24 and 72 hours after the event. Cold water therapy reduces DOMS pain by reducing the muscle inflammation and spasm that cause it. The principle is the same for treatment of acute injuries.
Cold therapy is used in both cases with proven benefits because the cause in both cases is tissue damage. Small micro-tears in muscle causes DOMS and large-scale tissue damage causes acute injuries. In fact, cold therapy delivered by a Coldtub™ is also an excellent treatment for acute injuries, even better than an ice pack or cold compress in many ways.