Just re-read your post; do I understand you correctly? There could be one club with colored belts and one without, but both would be part of the same association/federation/group?
Yup, I know in the USAF, although most dojos do the white/black and hakama after shodan for men and hakama for woman after their 5th kyu. I know some dojos vary and wear color belts, have a 6th kyu test, or wear hakama before shodan. There is no strict mandate that one has to follow but more of a recommendation.