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Chain molecules play important roles in industry and in living cells. Ourfocus here is on distinct ways of modeling the stiffness inherent in a chainmolecule. We consider three types of stiffnesses -- one yielding an energypenalty for local bends (energetic stiffness) and the other two forbiddingcertain classes of chain conformations (entropic stiffness). Using detailedWang-Landau microcanonical Monte Carlo simulations, we study the interplaybetween the nature of the stiffness and the ground state conformation of aself-attracting chain. We find a wide range of ground state conformationsincluding a coil, a globule, a toroid, rods, helices, zig-zag strandsresembling $\beta$-sheets, as well as knotted conformations allowing us tobridge conventional polymer phases and biomolecular phases. An analyticalmapping is derived between the persistence lengths stemming from energetic andentropic stiffness. Our study shows unambiguously that different stiffness playdifferent physical roles and have very distinct effects on the nature of theground state of the conformation of a chain, even if they lead to identicalpersistence lengths.

Chain stiffness bridges conventional polymer and bio-molecular phases}