What form of karate is based on striking?

Answer 1

The styles you are thinking of are Tae Kwan Do, and Northern Shaolin Kung Fu; Karate emphasizes economy of movement, so it frowns a lot on "fancy kicks." That is one thing all Karate styles are in agreement on, despite the differences of opinion on how to train and what is better to emphasize, Kata or Kumite. All Karate styles pretty much agree, fancy kicks are a big no-no; they waste too much energy, and precious seconds.

Answer 2

Karate of all types focuses on striking. It is one of the arts the makes that the primary study. That does not mean it does not include grappling techniques.