A narcotic is a drug which induces "narcosis" --drowsiness or sleep. Most often used to describe an opiate/morphine derivative, and I'm personally not aware of any that are not considered addictive, but some more so than others.
Not everyone becomes addicted though, any more than everyone who drinks becomes an alcoholic. Not even if used and/or abused on a long term basis. If they did, then a majority of college students would probably all become alcoholics, long before graduation.
Percocet is a combination of tylenol and Oxycodone, which is a morphine derivative. It has also become a very popular street drug that carries a rather high risk of addiction, resulting in it's nickname, "hillbilly heroin."
My brother was in a serious accident, where he was put on a morphine drip for several MONTHS. Afterwards, he successfully sued his doctors for his resulting addiction and subsequent rehab. bills, which amounted to over $60,000. That was over 15 years ago, and somehow, he's managed to stay "clean and sober" but even now, it's a constant struggle.
Again, that was over 15 years ago. Many doctors have become more cautious about prescribing narcotics on a long-term basis now. Aside from the risk of lawsuits from patients and/or surviving family members, if it can be determined that they have over prescribed these types of medications, they can be subject to legal sanctions and even lose their license to practice medicine.
Not all states (or countries) have a centralized database that advises doctors of every medication that may be prescribed to a patient, and there are addicts who will visit several doctors to obtain the quantity of narcotic drugs desired. When pills are prescribed, narcotics also run a greater risk of accidental death from overdose than most other medications because judgement may also become impaired. (Resulting in those lawsuits from surviving family members.)
An additional risk of using narcotics is they may give patients a false sense of "well being" which may result in taking actions that cause even greater injuries. For example, running on a sprained ankle--or eating certain foods that would normally cause severe distress, because they don't feel the pain that's trying to warn them to stop.
Pain is actually an important survival mechanism. If nothing else, it teaches us not to stick our hands in fire.
I was once given Demerol so I could perform on stage with strep throat, and I sang like a bird all night. But couldn't talk for 2 weeks afterwards, and was scared to death. Even my doctor couldn't tell me whether or not the throat damage from that stupid stunt was permanent. Fortunately, my voice did return.
Doctors who specialize in pain management will usually require frequent visits, so they can run tests and closely monitor patients who require narcotic medications on a long term basis.
But of course, all doctors are different and medical opinions on this subject differ as well.