Entropy plays a critical role in the long range structure of biopolymers. To model the coarse-grained chain entropy of the residues in biopolymers, the lattice model or the Gaussian polymer chain (GPC) model is typically used. Both models use the concept of a random walk to find the conformations of an unstructured polymer. However, the entropy of the lattice model is a function of the coordination number, whereas the entropy of the GPC is a function of the root-mean square separation distance between the ends of the polymer. This can lead to inconsistent predictions for the coarse-grained entropy. Here we show that the GPC model and the lattice model both are consistent under transformations using the cross-linking entropy (CLE) model and that the CLE model generates a family of equations that include these two models at important limits. We show that the CLE model is a unifying approach to the thermodynamics of biopolymers that links these incompatible models into a single framework, elicits their similarities and differences, and expands beyond the models allowing calculation of variable flexibility and incorporating important corrections such as the worm-like-chain model. The CLE model is also consistent with the contact-order model and, when combined with existing local pairing potentials, can predict correct structures at the minimum free energy.