As usual, unfortunate rumors, heresay and other unfounded descriptions have clouded the true historical facts surrounding Judo and Jujutsu.
1. Earliest Jujutsu
The historical origin of Jujutsu is debated and debatable because historical evidences and documentation are, at best, very scant. Contrary to the common view of a "martial art" today, however, it was most certainly not a "unarmed" self-defense system. Most likely, it developed into a series of techniques on weapon (sword, spear, dagger, etc.) retention and draw prevention, mainly involving swords.
2. "Transitional" Jujutsu
After the Meiji Restoration, the wearing of two swords by the Zi-Samurai was banned, leading to the gradual decline of the "ancient" Jujutsu involving weapons. Many transitional Jujutsu Ryu's developed that gradually switched emphasis to empty-hand techniques in response to the changing times. Still, one could easily see the sword/weapon influence (now done against empty-hands or "hand blades") of the earlier techniques. Daito-Ryu Aiki-Jujusu, as well as its descendant Aikido, betrays such an origin.
3. Modern Judo
Dr. Kano Jigoro modernized the transitional Jujutsu into a modern system, introducing such scientific concepts as ranks (belts), uniforms (Dogi), systematic curriculum and training as well as sparring (Randori) and contests (Shiai). In police-sponsored contests, Kano's Judo beat all comers from the transitional Jujutsu Ryu's that still relied on antiquated training methods (static, cooperative training and forms or Kata).
4. Olympic Judo
When WWII ended, Judo, along with all Japanese martial arts, was banned by the American occupation authorities. In an effort to "save" Judo from this fate, Kodokan (home of Judo) reformed Judo as a "sport," leading to the eventual adoption of Judo as an Olympic sport. Though the complete Judo curriculum remained "on the books," Olympic Judo emphasizes time limit and Ippon (total victory) based on a flawless throw. More "reforms" are on the way to make Judo "more exciting on TV."
5. Brazilian (or "Gracie") Jujutsu
Brazilian Jujutsu is a descendant of modern Kodokan Judo. It is most certainly not a Jujutsu Ryu in a traditional or transitional sense. While Kodokan Judo evolved into Olympic Judo, Brazilian Jujutsu evolved from modern Judo into a ground grappling and no-holds barred contest system. The entire extant Brazilian Jujutsu curriculum is a subset of existing Judo curriculum on the books. However, some such techniques (such as ankle locks, for example) have been significantly de-emphasized in, or removed from, Olympic Judo.