Hey Robert,
In regards to history, one must accept both the good and bad. We can not choose to acknowledge only certain elements of our history, and deny the rest.
Tien Dei Wui=Secret Societies
Hung Mun=Secret Societies
Saam Hop Wui (Triads)=Secret Societies.
They are all related. What you see as a major difference, I only see as a factor of time.
Besides, the term "Triads" itself is a highly generalized term. And refers to many many people from many different and distinct organizations that are considered "Triads".
Underground criminal organizations like you mention, such as the 14k in Hong Kong represent only one part.
There are also political members in the Triads. Like certain Taiwan politicians for example.
Also many Martial Artists are also Triad members. Not just those studying WCK.
Anyways, my point is that despite public perception, not all Triad members are simply criminals.
In actuality their membership is much more complex.
Best,
Alex