We report the first reliable prediction of the critical point (CP) (T-c, P-c, rho(c)) and two separate branches of the coexistence curve (CXC) for 10 alkali and alkaline earth fluids metals as well as for methanol. It is based on the recently proposed methodology of the congruent vapor-liquid (CVL) - diagram following from the developed earlier model of the fluctuational thermodynamics (FT). Both CXC-branches are predicted by the quite different (i.e. asymmetric and non-"symmetrized" artificially) FT-correlations. They are completely conformed in the asymptotic CP-region not only to the non-classical (with the exponent beta approximate to 1/3) projection of CXC on the (T,rho)-plane but also to the well-known classical Clausius-Clapeyron approximation of the vapor-pressure curve in the (P,T)-plane. The respective interrelations between two phase-dependent factors of thermodynamic similarity introduced, originally, by Riedel (Ri) and Trouton (Tr) in the classical principle of corresponding states (PCS) are estimated without any fitting. We show that neither any analytic expansion (it fails near CP) nor the known non-analytic Wegner's expansion (it diverges far from CP) are necessary to predict with the reasonable accuracy the entire range of CXC including its CP. The only input data for this aim are the standard low-temperature measurements of one-phase liquid performed at atmospheric pressure. The reasons of violation of the classical PCS for the metallic and ionic fluids have been analyzed. Despite the widespread belief on the contrary, FT methodology predicts the striking similarity of all studied fluid metals revealed by their CVL-diagrams. (C) 2017 Elsevier B.V. All rights reserved.