We find the connection between relativistic and nonrelativistic string vacua in AdS5×S5 in terms of a free parameter c flow. First, we show that the famous relativistic BMN vacuum flows in the large c parameter to an unphysical solution of the nonrelativistic theory. Then, we consider the simplest nonrelativistic vacuum, found in Fontanella and García [J. Phys. A 55, 085401 (2022)] (called BMN-like), and we identify its relativistic origin, namely a noncompact version of the folded string with zero spin, ignored in the past due to its infinite energy. We show that, once the critical closed B-field required by the nonrelativistic limit is included, the total energy of such relativistic solution is finite, and in the large c parameter it precisely matches the one of the BMN-like string. We also analyze the case with spin in the transverse anti–de Sitter directions.