Ideal magnetohydrodynamics is known to be inaccurate for the Earth's inner magnetosphere, where transport by gradient-curvature drift is nonnegligible compared to E¿B drift. Most theoretical treatments of the inner plasma sheet and ring current, including the Rice Convection Model (RCM), treat the inner magnetospheric plasma in terms of guiding center drifts. The RCM assumes that the distribution function is isotropic, but particles with different energy invariants are treated as separate guiding center fluids. However, Peymirat and Fontaine [1994> developed a two-fluid picture of the inner magnetosphere, which utilizes modified forms of the conventional fluid equations, not guiding center drift equations. Heinemann [1999> argued theoretically that for inner magnetospheric conditions the fluid energy equation should include a heat flux term, which, in the case of Maxwellian plasma, was derived by Braginskii [1965>. We have now reconciled the Heinemann [1999> fluid approach with the RCM. The fluid equations, including the Braginskii heat flux, can be derived by taking appropriate moments of the RCM equations for the case of the Maxwellian distribution. The physical difference between the RCM formalism and the Heinemann [1999> fluid approach is that the RCM pretends that particles suffer elastic collisions that maintain the isotropy of the distribution function but do not change particle energies. The Heinemann [1999> fluid treatment makes a different physical approximation, namely that the collisions maintain local thermal equilibrium among the ions and separately among the electrons. For some simple cases, numerical results are presented that illustrate the differences in the predictions of the two formalisms, along with those of MHD, guiding center theory, and Peymirat and Fontaine [1994>. ¿ 2001 American Geophysical Union