Are there different styles of kendo/kenjutsu?
Kendo is pretty much the same world-wide. Most dojos are governed by the International Kendo Federation (IKF), which grew from the Zen-Nippon Kendo Renmei (ZNKR, the All-Japan Kendo Federation). There is a second federation in Japan, not as popular, but the differences are more political than technical. There used to be hundreds of kenjutsu ryu; only two dozen or so have survived and they are mostly very small organizations. One of the oldest is Tenshin Shoden Katori Shinto Ryu. There is also Itto Ryu, from which much of modern kendo is derived.