We approach the problem of coil-globule transition dynamics numerically by Brownian dynamics simulations. This method allows us to study the behavior of polymer chains of varying stiffness and the effects of bending stiffness on chain morphology during the process of coil-globule collapse, imitating globule formation in poor solvent conditions. We record and analyze a three-stage process of globule formation for flexible chains: (1) nucleation, (2) coalescence of nuclei, and (3) collapsed globule formation. Stiffer chains undergo similar formation stages; however, the "raindrops" formed by these chains are elongated (unlike spherical structures formed by flexible chains) and exhibit regular packing of chains into antiparallel hairpin structures. In order to assess the transition dynamics quantitatively, polymer chain configurations were analyzed by generating contact maps and contact frequency histograms for all given configurations. These clusters are initial-configuration-dependent, and their growth and intercluster contacts have direct analogy with the process of raindrop coalescence.