High-T c cuprate, alkali-doped C 60 and several other unconventional superconductors have very high transition temperatures T c with respect to the energy scale of superconducting (SC) charges inferred from the superfluid density (SFD). The observed linear relationship between T c and the SFD can hardly be expected in BCS superconductors while being reminiscent of Bose Einstein Condensation of pre-formed bosonic charges. As additional non-BCS like behaviors, responses similar to those in the bulk SC states have been observed at temperatures well above T c in the vortex-like Nernst effect, diamagnetic susceptibility, and transient optical conductivity in recent photo-excited pump-probe measurements. In this paper, we propose a coherent picture based on equilibrium and transient SFD to understand these unconventional behaviors in cuprates, K 3 C 60 , and organic superconductors. This picture assumes: (1) Dynamic SC responses in the Nernst and photo-induced measurements emerge at the formation of the local phase coherence (LPC) among wave functions of pre-formed bosonic pairs. (2) Its onset temperature T LPC is distinct from and lower than the boson formation temperature often denoted as the "pseudo-gap temperature" T*, as T LPC is determined by the many-body boson density while T* represents attractive interaction between two fermions. (3) The bulk superconducting T c , signaling global phase coherence, is significantly reduced from T LPC , due to the competition between the SC and antiferromagnetic (AF) order. (4) The inelastic magnetic resonance mode (MRM) controls T c in the SC-AF competition. (5) The transient optical responses can be attributed to a change of the balance between the competing SC and AF orders caused by photo excitation. The assumptions (1) and (2) explain the relationship between T c and the transient SFD in photo excited studies and equilibrium SFD in Nernst effect. (3) and (4) are inferred from the linear dependence of T c on the MRM energy. (4) and (5) are consistent with the behaviors of the 400 cm -1 optical responses in equilibrium and photo-excited studies and temperature dependence of the intensity of this optical mode and the MRM. Unlike previous phase-fluctuation pictures which expect dynamic responses between T* and T c , the present picture involving competing order indicates that dynamic SC responses are seen between T LPC and T c .