We shall consider the similar and different properties of two closely related stochastic processes, namely, Cox-Ingersoll-Ross and Bessel processes, both of them being strictly positive solutions of the respective stochastic differential equations. Strictly positive values make them convenient to model real processes in physics, biology, economics. For example, in finances they are used to forecast interest rates and in bond pricing models. In our research we combine the methods of stochastic analysis and methods based on the explicit formulas for probability distributions of CIR and Bessel processes.