Is kungfu a part of karate?

The term "Kung Fu" describes the Martial Arts of China, and there are literally hundreds, possibly over a thousand different empty-hand, and weapon styles.

Karate refers to an Okinawa martial art that spread from there to Japan, Korea and the rest of the world.

It is my personal opinion, Karate is better for modern day life because it takes less time to master and include more strikes then a lot of basic Chinese martial arts.

If you want to become a martial arts master and a human weapon, then I would say Kung Fu, because of the enormous volume of styles available to you. Granted that you find a competent teacher.