  We present an analysis of all observations of Cygnus X-1 by the BATSE (20-300
keV) and by ASM (1.5-12 keV) until 2002 June, including 1200 days of
simultaneous data. We find a number of correlations between fluxes and
hardnesses in different energy bands. In the hard state, the variability can be
explained by softening the overall spectrum with a pivot at 50 keV and another,
independent variability pattern where the spectral shape does not change when
the luminosity changes. In the soft state, the variability is caused by a
variable hard tail of a constant shape superimposed on a constant soft
component. These variability patterns are in agreement with the
energy-dependent rms variability in the two states. We also study in detail
recent soft states in 2000-02. The last of them has lasted so far for >200
days. Their spectra are harder in the 1.5-5 keV band but similar or in the 3-12
keV band than those of the 1996 soft state whereas the rms variability is
stronger in all the ASM bands. On the other hand, the 1994 soft state
transition observed by BATSE appears very similar to the 1996 one. We interpret
the variability patterns by theoretical Comptonization models. In the hard
state, the variability appears to be driven mostly by changing flux in seed
photons Comptonized in a hot thermal plasma cloud with an approximately
constant power supply. In the soft state, the variability is consistent with
flares of hybrid, thermal/nonthermal, plasma with variable power above a stable
cold disk. The spectral and timing differences between the 1996 and 2000-02
soft states are explained by a decrease of the color disk temperature. Also,
based on broad-band pointed observations, we find the intrinsic bolometric
luminosity increases by a factor of 3-4 from the hard state to the soft one.
