Yes and no. As I understand it...the TKD Kwan founders, fo rth emost part, got a lot of their training in various Japanese/okinawan arts (shotokan being the biggest contributor). I belive that the founder of TSD also claims some chinese influence from time spent in Mongolia. I'll let the TSD historians sepak to that though.
The kwan founders returned to korea and oepened their schools. ultimately there was apush to unify the kwans. Many did, the TSD section ultimately did not....so, whle related, TKD did not descend directly from TSD. Rather they split off from the same related art(s). That's why I say more like an uncle than a father.
Peace,
Erik
Tang Soo Do is a blanket term, much as Karate-Do is. However, while there are a few other organizations under the blanket, it is most significantly used to name the decendants of the Moo Duk Kwan and it's curriculum.
The Moo Duk Kwan was founded in 1945 by Hwang Kee, originally teaching an art named Hwa Soo Do, consisting of whatever the Kwan Jang Nim had managed to pick up during his childhood in Korea and his travels through Manchuria. Variously, these are described as being a mimicry of Taekkyon, which the Kwan Jang Nim never claimed formal training in, Yang style Tai Chi Chuan, Shaolin Long Fist, and Dham Dui Sip E Ro (Twelve Step Springing Legs), but all of these are disputed, though the traditional curriculum of the Moo Duk Kwan contains hyung named for these arts, at least one of which is now lost. In any case, Hwa Soo Do was unfamilar to and unpopular with the Korean populace, and in 1947, Hwang Kee reformulated his art to use the familiar Japanese forms, while cross training with the Chung Do Kwan, and renamed what he was teaching Tang Soo Do, his art settling in parallel to the various other Kwans, with, perhaps, more of a Chinese influence.
With this new art, readily recognized by the Koreans as a martial art after the long occupation, the Moo Duk Kwan rapidly became a large and strong organization. When the call went out to create a national sport for Korea from the martial art organizations, Hwang Kee and the Moo Duk Kwan initially joined in the effort, though this eventually fell apart, and Hwang Kee formally withdrew the Kwan from the effort of the creation of Tae Kwon Do, though many of his students stayed with the new association. This is discussed further
here.
During approximately the same time frame, Kwan Jang Nim Hwang got hold of a copy of the Muyetobotongji, an old historical war manual, containing a large segment on 'Kwon bup', or fist techniques. Using this manual, he created fourteen new hyung, and renamed his art to Soo Bahk Do. That is rougly where it stands today, while a wide assortment of breakaways happened over time, creating the various small TSD organizations, clinging to the old name of the art. Each school will have its own little particulars, depending on when it broke from the Moo Duk Kwan, and how much of the latter curriculum it picked up... and what else it picked up along the way.
There is no direct line between Moo Duk Kwan Tang Soo Do and what is today called Tae Kwon Do. There have been many instances where one has influenced the other, for better or worse, but no simple way to say that one came from the other.