When discussing individual martial arts, using correct terminology is imperative. When I use the word "style," I am referring to a family of systems that share very specific common ground. In this sense, the correct response would be Karate, Taekwondo, Wushu (not Kung Fu), Jujutsu (correct English spelling), etc. Each of these styles has their own focal points which they have come to be known for. Karate is known for its emphasis on solo kata and close quarters striking, Taekwondo for its kicks, Wushu for its circular fluidity, Jujutsu for its grappling (standing and ground). None of these focal points even begin to describe the depth of what each system under their umbrella offers, but its a good starting point when trying to classify what system you study.
Characteristics: Strictly Japanese based. Physical techniques center around joint locks and manipulations, throwing and ground fighting. Limited striking to vital targets.
Systems: Daito-Ryu, Yoshin-Ryu, Takenouchi-Ryu, Hakko-Ryu, Judo, Aikido and more.
Characteristics: Strictly Korean based. Itself being a sub-style of Karate, it's known for its emphasis on kicking techniques and sport application. Demonstrations also frequently include breaking.
Systems: Chung do Kwan, Jidokwan, Oh do Kwan, Kukkiwon, Songahm, ITF and more.
Characteristics: Further divided into Okinawan and Japanese systems. Physical techniques center around striking and close quarters fighting. Emphasis on solo kata practice and body conditioning.
Systems: Goju-Ryu, Shorin-Ryu, Uechi-Ryu, Shotokan, Wado-Ryu, Kyokushin and more.
Characteristics: Strictly Chinese based. Further divided into internal and external systems. Physical techniques are often circular and fluid, equal emphasis on striking and joint manipulation.
Systems: Shaolin, Five Animals, Taijiquan, Bagua, Ch'uan Fa, Fu Jow Pai and more.
One thing you will find, however, is the deeper you study into your own particular system, the cloudier the lines become. If you know where to look, at their core every style teaches the same basic physical techniques. What defines an individual system may be slight technical variations, philosophies, applications, etc. but at the end of the day, we are all human and the human body is limited as to how many ways we can strike, twist, lock, throw and physically manipulate one another. In the end, it is all Budo (the path to enlightenment through the study of combat). The old Chinese proverb holds true, that "there are many paths up the mountain but once you reach the top the view is the same." It is important to know what you are truly studying, which is why proper classification and terminology is important when discussing it with others. What's more important is the journey. As a true student of Budo, you should be willing to get on the mat and train with anyone who has information to share regardless of what system they come from. As I see it, we're all just different branches from the same family tree.