  The high-mass accreting binary Cyg X-3 is distinctly different from low-mass
X-ray binaries (LMXBs) in having powerful radio and $\gamma$-ray emitting jets
in its soft spectral state. However, the transition from the hard state to the
soft one is first associated with quenching of the hard-state radio emission,
as in LMXBs. The powerful soft-state jets in Cyg X-3 form, on average, $\sim$50
d later. We interpret the initial jet quenching as due to the hard-state
vertical magnetic field quickly diffusing away in the thin disc extending to
the innermost stable circular orbit in the soft state, or, if that field is
produced in situ, also cessation of its generation. The subsequent formation of
the powerful jets occurs due to advection of the magnetic field from the donor.
We find this happens only above certain threshold accretion rate associated
with appearance of magnetically driven outflows. The $\sim$50 d lag is of the
order of the viscous timescale in the outer disc, while the field advection is
much faster. This process does not happen in LMXBs due to the magnetic fluxes
available from their donors being lower than that for the wind accretion from
the Wolf-Rayet donor of Cyg X-3. In our model, the vertical magnetic field in
the hard state, required to form the jets both in Cyg X-3 and LMXBs, is formed
in situ rather than advected from the donor. Our results provide a unified
scenario of the soft and hard states in both Cyg X-3 and LMXBs.
