There are many styles that are considered Shorin-Ryu. Shobayashi-Ryu is a specific type of Shorin-Ryu that has been passed down by a specific set of masters.
Many styles of Shorin-Ryu as well as other types of martial arts share some of the same roots, ideas, and aspects with Shobayashi-Ryu. In fact, some other styles even teach the same kata (although usually slightly different versions).
Here are just a few of the many styles of martial arts that share similarities with Shobayashi-Ryu.
Goju Ryu: This style was founded by Master Miyagi who was one of Osensei's instructors. In fact, at least three kata that I know of from are practiced in both styles. These are Seisan, Sanchin, and Seiuchin.
Uechi Ryu: This is another style that contains several of the same kata as Shobayashi-Ryu. The kata that the two styles share are Sanchin, Seisan, and the three Naihanchi kata.
Chuan Fa: A style of Kung Fu from Southern China, Chuan Fa has had a huge influence on Karate in general. In some styles the influence is more prevalent than others. Shobayashi-Ryu shows quite a bit of influence. It may sound funny to say, but many of our techniques were "made in China."
Qi Gong: Qi Gong is known as an internal style from China. This means that it focuses on loose flowing movements, breathing, and the development of your internal energy (also known as qi, or ki). Many of our stretches, breathing exercises, and kata come from Qi Gong or have at least been influenced by it.