The League of Six Kingdoms was the alliance of the Barraki, six conquerors and rulers (Pridak, Ehlek, Mantax, Kalmah, Carapar, and Takadox) who dominated much of the Matoran universe in ancient times.
The League was the initial employer of the Vortixx of Xia.
Pridak was the leader of the League of Six Kingdoms.
The members of the League of Six Kingdom's armies weren't members of the League itself, they were essentially mercenaries.
The League of Six Kingdoms was the name for the alliance between the Barraki.
The League of Six Kingdoms referred to a political alliance, Barraki referred to the individual leaders of the respective kingdoms involved.