The paper investigates the connections between the symmetries of the same dynamical system defined in spaces with various number of degrees of freedom. More precisely, we will consider a system defined in a n-dimensional space, we will apply the similarity reduction procedure, and we will compare its solutions with the ones of the same system projected in a n–1 dimensional space. Despite the fact that both cases lead to equations depending on n–1 independent variables, there are important differences in the behavior of the system. Some similarities can be also noticed. As a concrete example for sustaining these conclusions, the Burgers-Korteweg de Vries equation in 2 dimensions will be considered.