Since we would be considered "Old School", in terms of our TKD instruction, the primary self defense applications would be from Hapkido. The major difference between Hapkido and Original TKD, in simplistic terms, would be the amount of specific technique applications. Example: wrist techniques - In Hapkido they play a major role in the foundation of the art - thus the many variations of defending against a wrist grab. In TKD, understanding the principle of application and then reducing the tangable number(s) of expected variations is our positioning. Most styles of Hapkido have kicks, that folks say are different then TKD kicks. With the exception of the roundhouse kick, most if not all the practical long range kicks are similar, if not the same. Hapkido also uses short range kicks, but so does original TKD. Folks say Hapkido is primarily circular, but it also uses linear movements, so does OTKD. One primary difference IMO would be that some Hapkidoin go directly to a trap/catch of the attacker limb, whereas we would always deflect/redirect and strike before attempting the trapping/joint control technique. Another big difference would be in the breakfall area. In Hapkido, breakfalls are a major part of their training. In OTKD, we have that training also, but not to the extent that Hapkido places on it. Because we seem to do more initial striking before technique implementation, then what most Hapkido folks state they do, our attacker/training partner is not in an advantagous position to perform a breakfall. To be perfectly honest, the defender may not even get into a position to affect a joint lock/takedown or a throw, unless within the confines of training, we learn to adapt more control over the strikes we choose to use.
The Hapkido tapes of Fariborz Azhakh, who if not mistaken, is of the Sin Moo Hapkido lineage, looks almost identical to what we/I practice.