How are nsaid drugs such as celebrex (celecoxib) different from ordinary pain killers?

Work @ Injury. For the most part, these meds work at the site of inflammation which is causing the pain. They also have some effect on the brain's perception of pain but the main point of effect is at the area of injury. Injured tissues release toxins which the nsaid's retard the formation of in the local area.Celebrex (celecoxib) is unique from other nsaid's in that it does not thin the blood.
Treats a problem. Celebrex (celecoxib) is actually not an analgesic agent. It helps decrease the inflammation and hence might help decrease one of the causes of pain. Many people need both since they work very different.