A generalized adiabatic connection that applies to any type of range-separated hybrid (RSH) functional employed within generalized Kohn–Sham (KS) theory is presented. This generalized relation is then used to derive a definition for a rigorous distinction between multiplicative exchange and correlation components. The developed adiabatic connection is defined in terms of both generalized and conventional KS orbitals. It is shown, however, that using only the KS orbitals produces an error that is (Formula presented.), where (Formula presented.) is fully defined in terms of parameters in the RSH functional, and is found to be small in practical calculations. It is expected that this new adiabatic connection can assist in the development of new RSH functionals and the assessment of existing ones.