Each school (kwan) had a little bit different way they practiced and taught because of the head instructor's background. One school may teach karate from Funakoshi's-lineage, one may teach chuan-fa and Shudokan karate, etc. So, their tradition and practice was different from each other.
Jido Kwan was a kong soo do (karate) school. The headmaster, Yoon Kwye Byung, learned karate in Japan from Kanken Toyama. He even included bong hyung (staff forms) in the curriculum and he wrote a book about it in the 1940's. - I've never met any school claiming Jido Kwan nowadays that knows any bong hyung from this lineage. They practiced at a place that had yudo(judo), but there wasn't really any Hapkido around at that time to influence them. It may have been someone later down the line that added it.
Chang Moo kwan's headmaster was Byung In Yoon, who studied Chuan-fa while growing up in Manchuria and shudokan karate from Kanken Toyama in Japan. So, this school had forms and techniques from both styles in the curriculum. One of the old-days (1951) students of this school described to me the appearance of the students as, "Hard but smooth, smooth but hard." This makes sense with the chuan-fa influence of deflecting/redirecting blocks and techniques, contrasting the harder force-against-force blocks from the karate influece. Byung In Yoon and Jido Kwan's Yoon Kwye Byung were good friends since their college days in Japan. Chang Moo Kwan even had one of Jido Kwan's bong hyung (staff forms) in the curriculum.
In short, each kwan had a little bit different influence, thus different instruction and tradition. But now, they all look the same and practice modern forms created in the late 1960's and early 1970's. If a school claims a old kwan name, yet practices Palgue, Taeguek or the Yudansha forms (Koryo, Tae Baek, Ship Jin, Jee Tae) as their only forms, they are not really teaching the old material. Could be, that their instructor's instructor, etc. was originally from that old kwan - but nothing in the curriculum remains from the old tradition. Does this make sense?
R. McLain