don't think any of them are true federations, at least at the national level and below.
but as far as bodybuilding organizations, there is the IBFA, IDFA, IFBB, INBA, Musclemania, NABBA, NAC, NGA, NBI, NASF, OCB, SBF, UNBA, USBF, WABBA, WNBF, WPF, and probably a dozen more.
The top three are probably IFBB, NABBA, and WNBF. WABBA is big in Europe.