This talk aims to provide a bridge between numerical contractivity analysis of dissipative stochastic differential (SDEs) and partial differential equations (SPDEs). The accurate long-term numerical preservation of the dissipative character of stochastic dynamics is a relevant issue in stochastic geometric numerical integration, not only because it provides feasible approximate solutions more tailored to the reference problem, but also because it has several implications with many other issues, such as the analysis and computation of invariant measures, ergodicity theory for stochastic partial differential equations, nonlinear stability issues and so on. The talk first introduces the numerical analysis of mean-square contractivity, both for additive and multiplicative noise, assuming that the stochastic partial differential equation is of reaction-diffusion type. The results are proved in a general framework for the diffusion operator and under weak hypotheses on the reaction term. The theoretical inspection is equipped by selected numerical examples on relevant problems in the literature, confirming the strict dependence of numerical contractivity on the CFL condition characterizing the numerical solver. To some extent, if in the SDEs case the crucial role is covered by restrictions on the time step, in the SPDEs case the CFL condition dictates the contractive character of the numerical dynamics.