abstract: A growing number of biological, soft, and active matter systems exhibit normal diffusive dynamics with a linear or practically linear growth of the mean-squared displacement, yet with a non-Gaussian distribution of increments. The distribution of the displacements' projections on a given axis is, at shorter times, often quite close to the Laplace (two-sided exponential) distribution. Such behavior can be attributed to the inhomogeneity of tracers (pure superstatistics), or to fluctuations in, or to inhomogeneity of the environment, in which the diffusion takes place. In the last two cases the long-time behavior of the displacements' probability density is Gaussian. We discuss the situation in some detail especially paying attention to similarities and differences between the last two cases, and to the possibilities to tell one apart from the other.