Are benzos a narcotic

No. A narcotic is an opiod based anagesic indicated for the treatment of moderate to severe pain. Some common examples would include Codeine, Hydrocodone, Oxycodone, Morphine, etc.

A benzodiazepine is a distinct chemical class of drugs designed to treat, amongst other things, panic disorder, anxiety, insomnia, and in some cases, seizures.

While both drugs are controlled substances in most countries and both can be highly addictive, they are distinct from each other and do not build cross tolerance for each other. These drugs will, however, build tolerance with continued use and cross tolerance is commonly seen (someone on morphine for a long time will experienced a diminished effect with it; that reduced effect will also be seen with hydrocodone).

In the USA, most Benzodiazepine drugs are schedule IV, while Narcotics can range from I to V depending on the strength and abuse potential.