[en] The critical behavior of a Curie-Weiss model may be obtained from the standard Landau expansion, in powers of the magnetization order parameter m, from the functional ψ(T,H;m) = -Hm + pound(T,m), where pound is the Helmholtz free energy. As an alternative procedure, the Gibbs free energy, g(T,H), is obtained as the minimum of a functional g(T,H;y) with respect to a continuous spin field y and the critical behavior is analysed from an expansion of this functional in powers of y. We show that, in spite of displaying quite distinct coefficients, both expansions lead to the same critical behavior. The Ising ferromagnetic model is discussed in detail for pedagogical reasons. We also obtain the relations between the coefficients of the two expansions for a more general case. We remark that these distinctions are already present in different strategies to obtain a suitable Landau-Ginzburg-Wilson hamiltonian for performing a momentum-space renormalization-group calculation. (author)