The term Kuk Sool (National Martial Art) does not describe a single art but the combination of many arts primarily being Korean in nature.
The Kuk Sool HapKiDo, Kuk Sool Won, Kong Shin Bup, Hwa Rang Do and other Korean Martial Arts systems are derived from the same base arts with Korean, Chinese, and Japanese influence. (See Kong Shin Bup
Kuk Sool Hapkido and Kuk Sool Won are nearly the same art. You will find Kuk Sool Won popular within the U.S.A. under GM Suh, In Hyuk and Kuk Sool HapKiDo popular in Korea under Seo, In Sun. Even though the spelling of the last names are different the Suh/Seo Grandmasters are brothers. The main difference between the two associations is tha the WKSW requires it's members to follow a much more strict set of political guidelines.
The main difference between a typical HapKiDo curriculum and a Kuk Sool curriculum is the inclusion of empty hand and weapon forms in the Kuk Sool arts.