We present a complete analysis of the heavy to heavy and heavy to light baryon semileptonic decays in the heavy quark effective theory within the framework of a Bethe-Salpeter (B-S) approach and demonstrate the equivalence of this approach to other work in the field. We present in a compact form the baryon B-S amplitudes which incorporate the symmetries manifest in the heavy quark limit and which also show clearly the light quark dynamics. A similar form of the B-S amplitude is presented for light baryons. Using the B-S amplitudes, the heavy to heavy and heavy to light semileptonic baryon decays are considered. As expected there is a dramatic reduction in the number of form factors. An advantage of our B-S approach is demonstrated where the form factors are written as loop integrals which in principle can be calculated. (author). 15 refs, 3 figs, 2 tabs.