Not any expert, but I know soreness at the time of exercise when muscles are exerted it is due to lactate acid and oxygenation. That again is when the muscles are being worked. I believe that is why less reps and more sets is recommended when beginning. Or, that at least is how it was explained to me when cross training for cross country / track during college.
The soreness after exerting muscles the next day is a different event taking place with the muscles. The muscles are not requiring the transformation of glucose for energy along with oxygenation. It could be said they are simply sore and rest is needed for recuperation. Or, as is suggested a minimum of one day and best two days between exercising the same muscle groups again.
Tylenol works for me with muscle pains and so does Alieve. That of course IMHO is tricking the brain essentially. I am not an expert in the field of pain. Another oddity to consider if you like to ponder stuff is the location of the brain for pain does not care if it is emotional pain or physical pain. Pain is simply pain.
But, oddly studies are being conducted to determine if emotional pain triggers sensations of physical pain as a mechanism for relief psychologically speaking. Or, there is an emotional pain and it is manifested as a physical pain.
Maybe it hurt emotionally when working out and it is manifested physical. Or, just speculating the emotional pain of not being as strong as once or as thought would like to be (reality principal) is actually painful emotionally.
It is experienced through the body exercised with memory of pain - lactoses. The pain of the exercising when lactoses does occur is remembered in the pain center of the brain and felt at that body part later while emotionally dealing with that reality of weakness (reality principal).
As strengthening the muscles occurs with more being achieved and much easier, well, confidence occurs. Lactoses is lessened as the process of metabolizing glucose and oxygenation changes. As confidence occurs emotional pain is lessened offering less or no after effects of pain. One becomes stronger overcoming pain both physically and emotionally. The pain center does not care since pain is pain.
Remember I am not an expert of these things. Those suggested above are speculative from reading over the years. And, most certainly insert the typical disclaimer here :)