In North America, Brazilian Jiu-Jitsu practice and instruction is quite different from what is found in schools of Jiu-Jitsu that describe themselves as Japanese.
Are the two martial arts still related? Is training in one still recognized in the other?
Most people acknowledge that, given that Brazilian Jiu-Jitsu is derived from Maeda's teachings in Kodokan Judo (then known as Kodokan Jiu-Jitsu in the appropriate romanization of the time), it is recognized as a derivative of Judo, but they have each long-since taken very different paths.
Jujutsu (the modernly accepted romanization of 柔術) is a broad term used to describe a large number of various styles/schools (ryuha) of unarmed combat, and the rather generic description of "Japanese Jujutsu" used by dojo marketing gurus is usually just a collection of common techniques from those schools mixed with Judo, or, in rare cases, a marketing ploy to make a single ryuha appear more familiar (People may not recognize, for instance, Yagyu Shingan-ryu Heiho [poor example, since most people would doubt it's even jujutsu at first glance], but the broad term of "Jujutsu" or, with the modern upsurge of BJJ, "Japanese Jujutsu" [to differentiate] is easily more accessible). Brazilian Jiu-jitsu is very distantly related to these arts.