Acetaminophen is an analgesic (Pain affector). Ibuprofen is an anti-inflamatory. The latter is better for muscle aches and pain because it corrects the reason for the pain - the inflamed tissue. When the inflamation goes down, it prevents the muscle or tissue from reinjuring its self simply because it is inflamed/swollen. A side effect is the pain is reduced. With many injuries, just having the site or tissue swollen can perpetuate injury (think a slipped disc or torn ligament, or torn muscle). Many times patients are instructed to keep the ibuprofen on board regularly to prevent the inflamation from returning, thence to need to keep re-reducing the inflamation after it re-swells if one lets the ibuprofen wear off. Ideally, keep it going so it doesn’t wear off.
Sore achy muscles after strain or exercise are usually because of micro-tears, which then heal and become stronger, and anti-inflamatories are perfect for reducing the inflamation and allowing the healing to happen quicker. The reason you are sore-er the day following exercise is that over that period of time between the injury and the next day, the tissues have swollen or become inflamed. Profolactically taking an anti-inflamatory isn’t entirely necessary, but taking one soon after the exercise is helpful.