As for Shinkage Ryu / Yagyu Shinkage Ryu, at the same time they are both the same and different. The original Shinkage Ryu, as it was founded under Kamiizumi Nobutsuna, was/is a sogo bujutsu—an integrated battlefield combative system—and includes yari, tachi, odachi, kogusoku, naginata, bo, etc. The Yagyu family was taught only the tachi (kenjutsu), and they added on other attributes over time. Eventually, the full Shinkage Ryu syllabus of Kamiizumi was also brought into the Yagyu family course of instruction. However, the distinction between the Yagyu and Shinkage versions were/are maintained. In kenjutsu, for example, the most well known kata is called Sangaku-en. There are actually two Yagyu versions of Sangaku-en - Edo and Owari. In addition, there are two Shinkage Ryu versions - koden ("old transmission") and odachi. While there are similarities among all the versions, they are still kept distinct. All four are still maintained and kept distinct within the Kanbe line and possibly the Yagyu family line as well.
Both the Yagyu family line and the Kanbe line are members of the same koryu organizations in Japan and often do enbu at the same taikai. However, for reasons of etiquette, the Kanbe line is always introduced as Owari Kan Ryu, which is the spear tradition that is also part of its tradition.