When talking about BJJ, Judo, Kosen-Judo, among others, it is necessary to differentiate what is "sport", that is, the application of certain techniques under a certain set of pre-established rules; and what is "martial art", that is, the set of techniques that can be applied in any fighting situation that someone may be involved in.
When we talk about sport, then Kosen Judo and BJJ are different things, each modality is governed by different institutions, have different rules, and therefore, are different things.
But when we talk about martial art, then it's the same thing.
The BJJ is a lineage that began with Jigoro Kano and developed outside Japan, alternatively to the Japanese lineages. However, even being developed in extremely distant locations, the techniques, fundamentals, and all, are the same.
People outside Brazil usually believe that the BJJ is an adaptation of Judo performed by the great master Helio and transmitted to his family, but this version is just a markenting propaganda, as the techniques of Jiu Jitsu were taken to the world. by Gracies through the UFC show.
But Brazilian Jiu Jitsu has its origins in the Brazilian Marines. During the early twentieth century sailors were trained mainly in boxing and capoeira, were very tough and unruly, carried out many riots and the only way the officers found for the situation was physical punishment (lashing, whipping, etc.). Thus the Brazilian government, with good relations with the Japanese Empire (Brazil is the country with the largest Japanese immigration) seeing that the Nipponic Armed Forces were trained in Kano Jujutsu (Judo), decided to start a training program of this martial art with the marines.
In 1908 the navy rescued a group of Japanese from a wreck, among them was a Kodokan teacher, Sada Miyako, who spent a year teaching Judo / Jiujitsu to Brazilian sailors, with the intention of forming a training program that from 1909 began to be applied in the training curriculum. So before the Gracies there were already Jiu Jitsu based fighters in the country.
An important marine in the history of Jiu Jitsu was Luiz França. He learned the basics of martial art in the navy, then became a student of the first teacher to establish a Judo / Jiu JItsu academy in Brazil in the Amazon, Soshihiro Satake. He later became a student of Maeda (Count Koma), in the same class as Carlos Gracie, in the state of Pará, for four years, and later of Jyoji (Geo) Omori, in Rio de Janeiro. So the learning of France was much more solid and much longer than the learning of the Gracies.
Luiz França became a Jiu Jitsu teacher in the Navy, and it was there that he trained another important personality, Oswaldo Fadda, a young Marine who was his best student and intellectual heir in France. After leaving the navy he established a gym (Fadda de Jiujitsu Academy) on the outskirts of Rio de Janeiro, and held a dispute against the Gracie Academy in which they emerged victorious.
So the BJJ has these two main lineages: the Gracie lineage and the Fadda lineage, and all the teachers practically learned in one of these two. So the techniques taught and applied by all Jiu Jitsu fighters are those imparted by Kodokan masters: Sada Miyako, Soshihiro Satake, Mitsuyo Maeda and Jyoji Omori. It is even a mistake to call the art "Brazilian jiu jitsu" since its roots are Japanese, so in Brazil it is only called "jiu jitsu".
Now, the importance that the sporting aspect has taken on both Judo and Jiu Jitsu has brought a certain deficiency for practitioners, especially for those struggling interested in competitions and championships. A Jiu Jitsu fighter today is very deficient in standing fighting, just as a Judo athlete is very deficient in ground fighting, as most train thinking on the rules and forms of fighting in the competition, although the set of techniques belong to both modalities.