The overwhelming majority of those who train Jodo today are training ZNKR Seitei Jodo, the forms that were put together in the late 1960s for the Japanese Kendo Federation ZNKR.
They practise basic techniques and the twelve forms of seitei kata. The more experienced usually also train kata from Shindo Muso Ryu.
Technical details, how the forms should be carried out, details of the important points, are determined and described by ZNKR, and spread internationally via Kendo Organizations.
Other, far fewer, train Shindo Muso Ryu as Koryu, in a line of tradition that is passed from teacher to student. (Lat.tradere = transfer)
The forms are not forms as a series of techniques that can be described in a rulebook, but they are part of a system, a whole in which techniques are just one of many elements.
It requires personal relationship between teacher and student.
Each technique has its performance and its purpose, it is not certain that what is easiest to describe is what is most important.