What Is this style of fighting training? Can someone explain?
Ninjitsu/Ninjutsu is a system of guerrilla and commando warfare & espionage training used by the samurai and various other groups from mercenaries & bandits to peasants and priests. No system of ninjutsu is proven dispite internet claims and excuses. Hatsumi has never proven his ninjutsu line, but and neither have anyone else, for that matter. Takamatsu was even called a fraud much like Ashida Kim and Frank Dux are today so go figure where you would like to place your faith in a Ninjitsu lineage.
It should also be noted that the last known Koga Ninja (Seiko Fujita) was no more the Soke of all Koga styles then Hatsumi is the head of all Iga styles. Seiko was only the Soke of Wada-family Koga Ryu Ninjutsu. That said, all that matters (least to me) is effectiveness, so if it works use it and don't worry about what its called. However, I wouldn't call a kung-fu system ninjutsu even if was used by a ninja-like group such as the Mushin Naran or Lin Kuei. Course there is also an interesting question about hybred styles of ninjitsu where it becomes mixed with other systems.
Would you call ninjutsu, karate, judo and kung-fu sololy one of those arts or could it be defined as all of the above?
I learned a style of ninjitsu which came from a Japanese fellow, whose father moved to Canda after WW2. According to him many ninjutsu styles origionated as this (abridged general history); peasants were conscripted in military service to make the bulk of an armies foot soldiers. They were conscripted and not professional soldiers but were lead by Ashi Garu who were profession soldiers in peace time but not quite Samurai. Many of these peasants were organized into guerrilla groups to resist invasion. Several Samurai were recorded to also be Ninja & many bandits were proclaimed to be ninja simply by their level of successfulness. Ninjutsu as a commando, guerrilla and/or espionage system was a form of warfare often studied by samurai and a collection of techniques invented by other groups. Generally speaking on the Bujutsu subset styles were recorded historically & to be honest for all I know he could be BSing me. It works and I don't care about history as much as I care about effectiveness...