We report dynamic Monte Carlo simulations of polymer crystal growth induced by a template layer in the melt and semidilute solutions. The molecular simulations evidenced intrinsic regime transitions in the temperature dependence of crystal growth rates, which have been interpreted on the basis of the Lauritzen-Hoffman model, a specific model among the diverse points of view on the general mechanism of polymer crystallization in the literature. We found that, corresponding to the regime II-III transition, there exists a morphological transition from single to multiple lamellar crystal growth, implying the style of spherulite formation changing from a sequential filling to a completed inner filling at low temperatures. Meanwhile, stem-length distributions in the crystallites also exhibit a shift. Dilution makes more perfect chain-folding upon crystal growth, in accord with experimental observations. However, we could not observe the predicted smooth crystal growth front in regime I. In addition, contradictory to the previous expectation, the probability of adjacent chain folding increases slightly at low temperatures. We proposed a new interpretation of regime transitions on the basis of the intranzolecular-crystal-nucleation model for a better understanding of both experimental and simulation observations.