system
Given the following post, respond as if you're commenting on Reddit:
human
Why do pain relievers (NSAID/acetaminophen) relieve chronic pain while seemingly not affecting acute pain?

On the rare occasion I have a headache, I'll often reach for a Tylenol to help relieve the pain.

Usually this is relatively effective. Either it'll eliminate the pain completely or reduce it to a much more manageable level. 

Yet, even under the effects of something like Tylenol or Ibuprofen, if I were to say, pinch my arm, I'd still feel essentially the same amount of pain as normal. 

Is there a biochemical reason for this? Is there a difference between acute and chronic pain? Or is there perhaps some psychological component to it?
gpt
Pain is a pretty complicated topic- we can think about it in terms of what type of pain is going on- pain due to painful stimulus where nerves directly conduct an impulse/message  (pinch/cut), inflammatory pain (inflammation process) or due to damage to nerves (neuropathic).
Ultimately pain is the body’s ability to sense that something is wrong. 

NSAIDs and Tylenol work on reducing the production of prostaglandins and other inflammatory mediators. Prostaglandins are released during inflammation and help bring different types of cells to an area of the body to help fix the site if there is trauma or fight an infection. They do this through various ways including making blood vessels in the area more “leaky” so those cells in the blood can get to the site. Inflammation is basically the way the body can make sure an infected or hurt part of the body is getting the attention it needs. 

When you pinch your skin you are directly affecting causing pain receptors in your skin to fire (there are several types, this would likely be Ad fibers “pin prick, sharp pain”). This signal is conveyed immediately through nerve conduction. If there is sufficient trauma it can cause an inflammatory response, but if not the pain will subside with removing the stimulus. 

Headaches are a tough subject- there are many types. The most common type is a tension headache, where muscles in the neck and head are chronically stressed and can causes inflammation and pain. This is why NSAIDs can work for this type of headache.
Migraine and cluster headaches are caused by other processes and thus require different treatments.

Opioids reduce pain by slowing down signals of nerve conduction in the brain, but would not directly help with inflammation. 
It’s important for us to detect pain so we can address an issue - trauma/cut or a more chronic inflammatory issue.