We demonstrate that semiflexible polymer chains (characterized by a persistence length l) made up of discrete segments or bonds of length b show at large stretching forces a crossover from the standard wormlike chain (WLC) behavior to a discrete-chain (DC) behavior. In the DC regime, the stretching response is independent of the persistence length and shows a different force dependence than in the WLC regime. We perform extensive transfer-matrix calculations for the force-response of a freely rotating chain (FRC) model as a function of varying bond angle gamma (and thus varying persistence length) and chain length. The FRC model is a first step toward the understanding of the stretching behavior of synthetic polymers, denatured proteins, and single-stranded DNA under large tensile forces. We also present scaling results for the force response of the elastically jointed chain EJC model, that is, a chain made up of freely jointed bonds that are connected by joints with some bending stiffness; this is the discretized version of the continuum WLC model. The EJC model might be applicable to stiff biopolymers such as double-stranded DNA or Actin. Both models show a similar crossover from the WLC to the DC behavior, which occurs at a force f/k(B)T similar to l/b(2) and is thus (for polymers with a moderately large persistence length) in the piconewton range probed in many AFM experiments. We also give a heuristic simple function for the force-distance relation of a FRC, valid in the global force range, which can be used to fit experimental data. Our findings might help to resolve the discrepancies encountered when trying to fit experimental data for the stretching response of polymers in a broad force range with a single effective persistence length.