True Taiji Transmission
The further back in time we look, the more obscure the history of Taiji becomes. Yet from the study of this past, two things become clear. Firstly, that the inner essence of Taiji flows down from genuine teachers to sincere pupils in unbroken chains. Secondly, that each teacher must devise his or her own training system to express and pass on this impersonal inner teaching. The teaching must evolve outwardly or die inwardly. Yang Cheng-Fu developed the Yang Style Slow Form. Cheng Man-Ching created the Yang Short Form, and shifted the emphasis from fighting to internal harmonisation. Master Huang Xingxian created the Five Loosening Exercises, systematised 18 patterns of pushing-hands, and included the Sanfeng Quaiquan (Quick Fist) - a fighting fast form with ancient roots. While pupils under Master Huang's direction, we learnt and taught his system. Now, the training system we teach arises from our own individual understanding.
True Taiji has no Name
In former times Taiji was developed and practised within the Chinese communities of the world but its source is beyond the limits of race. In the old days in China, teachers with a good Art would seldom teach outside their own family or clan. This was for self preservation in a competitive and dangerous world. Consequently, methods could then be associated with the common family name of the clan. Now that fear is no longer a major factor in the transmission, open minded Masters recognise that the best potential may be found outside their own clan. Family names now serve little purpose. It is only a hindrance to the peaceful teaching and learning of Taiji to give undue importance to the various styles - Yang, Wu, Chen and other lesser known variations, or to claim some generational family link back to that styles founder. This is all attachment to outer form and is the mark of those who are young in the inner aspects of the Art.
True Taiji Lineage and Transmission
Master Huang Xingxian (Huang Sheng-Shuan) - deliberately taught his art widely and freely, for the sake of the art, the sake of the students and, as he explained, to prevent anyone claiming sole transmission and using that for self promotion. When a person passes beyond the external or body level their inner understanding should no longer be concerned with the name or outer form of the style. On the 3 internal levels these outer differences progressively have no meaning. Beyond the Mind they do not exist. As for beginners and the psychologically insecure, let them debate the relative merits if they feel compelled to do so. A practitioner's, teacher's or master's ability stands by itself with no consideration for name, race or title. Taiji arose in China but belongs to the Earth.
3 types of Taiji.
There is genuine traditional Taiji, 'healing' Taiji or 'gymnastic' Taiji. In traditional Taiji students progress through a long serious training, which produces true inner evolution, a deep well being and some ability at self-defense based on sensitivity and internal power rather than external strength and speed. The sublime experience of the past great practitioners is passed down, which requires effort from both students and teachers. The teachers have themselves been through such long training previously, with their own genuine teachers.
Secondly there is "healing" Taiji where people practice lightly to feel outwardly better and recover from the pressure of work and daily life. Like modern 'Yoga", there is some external value in this but it does not lead to internal refinement.
Thirdly you may also see "gymnastic" Taiji where all esoteric training is scorned and either beautiful "wushu" postures, or rough fighting movements are trained, perhaps with silk uniforms, sometimes for competition. This Taiji was officially promoted over the last 60-70 years but perhaps has lost the refined subtlety of the original art.
These last 2 methods are typically taught merely as a means of making a living. The lightly trained instructors, easily create new movements and systems which propogate their own simple ideas. These methods may increase attachment to and identification with the body (consolidating the ego). This is a long way from the great purpose of the deep and subtle art of true Taiji.
I suggest you think twice before investing your time in these last 2 - ask yourself what is really important in your life, then stay true to that and make your choice.