Yes and No. The primary influences of karate can be traced back to a single area, but as it 'travelled' from country to country, local skills were mixed in to create something different. Karate originated on the island of Okinawa, now a part of Japan. It was created by combining the local Okinawan art of Te with influences of Chinese Kung Fu.
Several hundred years later, Okinawan teachers went to Japan and taught karate there. Elements of the existing martial arts were incorporated and merged to become various styles of Japanese Karate.
From Japan, karate was taught in Korea, merging with the native martial arts there to develop a slightly new style. Each of the styles puts the focus on slightly different things. But if one watches a variety of skilled practitioners, you will begin to see differences and similarities between the different branches. But the ultimate goal of all karate-ka is to become a better person.