A consistent and unified microscopic theory of superfluidity and superconductivity is developed on the basis of two-stage Fermi-Bose-liquid (FBL) (in particular case, one-stage Bose-liquid) scenarios. It is shown that these phase transition scenarios is accompanied, as a rule, by the formation of composite bosons (Cooper pair and bipolarons) with their subsequent single particle (SPC) and pair condensation (PC). A brief outline of the modified and generalized BCS-like pairing theory of fermions is presented. In an analogy to that, a detailed boson pairing theory is developed. The SPC and PC features of an attracting 3d- and 2d-BG as a function of the interboson coupling constant in the complete range 0≤T≤T_B is studied in detail. It is argued that the coexistence of the order parameters of attracting fermions Δ_F and bosons Δ_B leads to the superfluidity (in³He) and superconductivity (in superconductors) by two FBL scenarios. One of these scenarios is realized in the so-called fermion superconductors (FSC) and the other in the boson superconductors (BSC) in which the gapless superconductivity is caused by the absence of the gap Δ_SF in the excitation spectrum of bosons and not by the presence of point or line nodes of the BCS-like gap Δ_F. The new adequate definitions for basic superconducting parameters of FSC and BSC are given. The theory proposed is consistent with the experimental data available.