It has nothing to do with Guns if you think that!
The "Shooting" in shootfighting or Shooto as its called in Japan, is when you "shoot" for the opponents legs for a takedown!
You can ofcourse win by TKO but mostly you win by Submission!
You cannot work the small joints like fingers, toes etc..
Ankles, Knees, Elbows are allowed though! As well as choking out your opponent! Opponent can tap whenever, saying that he wants to give up.
In Shootfighting you combine the Art of Striking (using Muay Thai training mostly) and the Art of Grappling (Submission Wrestling and/or Jiu Jitsu).
The Brazilians have developed a different sort of Jiu Jitsu than the Japanese, which they call Brazilian Jiu Jitsu (BJJ) and the Gracie Family with Helo Gracie developed their own Jiu Jitsu called Gracie Jiu Jitsu (GJJ).
A Well known Brazilian ShootFighting team is Chute Boxe with fighters such as Wanderlei Silva, Anderson Silva and Pele Landis Jons(He left Chute Boxe tho).
ShootFighting is a Sport that is a good example of Cross-Training (Training Muay for Striking and JJ for Grappling).
During the Age when Traditional Martial Arts was the most popular (60-70's) a fellow who was a trend-setter in Cross-Training was the late Bruce Lee!
He used his old Wing Tsun (which he started training first), and combined it with Boxing, Wrestling etc and in the end created his own style, Jeet Kune Do.
How did i get to Bruce? Oh yes! Cross-Training.
Nowadays MMA (Mixed Martial Arts) is very popular, especially for those who wishes to compete in full contact!
The K-1 contests are purely striking and resembles Thai Boxing contests OMGIAMRETARDEDCAUSEALOTISTWOWORDS, with some modified rules (Short Clinch, only one knee in the clinch, no ELbows etc) which is the number one competition for pure strikers.
In K-1 you are not allowed to grapple or fight on the ground etc...
The ultimate MMA contest In my Opinion is Pride, with UFC (Ultimate Fighting ChampionShip) second. Then we have Shooto(lighter weights), Pancrase etc...
Why prefer MMA before pure striking? Well, in my opinion, it is the closest you can get to a real fight in a sport. Pride have very good rules and is the ultimate for those who can fight both standing and on the ground.
If you are interested, i can send you to an FTp where you can see for yourself!

MMA in action!
Another good thing with ShootFighting and MMA in general is that it is also well implemented as self-defence on the Streets!
You have tools both for standup combat as well as groundfighting!