The statistical and distribution characteristics of the responses of a floater and its mooring lines are essential in designing floating/mooring systems. In general, the dynamic responses of offshore structures obey a Gaussian distribution, assuming that the structural system, and sea loads are linear or weakly nonlinear. However, mooring systems and wave loads are considerably nonlinear, and the dynamic responses of hull/mooring systems are non-Gaussian. In this study, the dynamic responses of two types of floaters, semi-submersible and spar platforms, and their mooring lines are computed using coupled dynamic analysis in the time domain. Herein, the statistical characteristics and distributions of the hull motion and mooring line tension are discussed and compared. The statistical distributions of the dynamic responses have strong non-Gaussianity and are unreasonably fitted by a Gaussian distribution for the two floating and mooring systems. Then, the effects of water depth, wave parameters, and low-frequency and wave-frequency components on the non-Gaussianity of the hull motion, and mooring line tension are investigated and discussed. A comparison of the statistical distributions of the responses with various probability density functions, including the Gamma, Gaussian, General Extreme Value, Weibull, and Gaussian Mixture Model (GMM) distributions, shows that the GMM distribution is better than the others for characterizing the statistical distributions of the hull motion, and mooring line tension responses. Furthermore, the GMM distribution has the best accuracy of response prediction.