  It is shown, using results of recent direct numerical simulations, laboratory
experiments and atmospheric measurements, that buoyancy driven turbulence
exhibits a broad diversity of the types of distributed chaos with its stretched
exponential spectrum $\exp(-k/k_{\beta})^{\beta}$. The distributed chaos with
$\beta = 1/3$ (determined by the helicity correlation integral) is the most
common feature of the stably stratified turbulence (due to the strong helical
waves presence). These waves mostly dominate spectral properties of the
vertical component of velocity field, while the horizontal component is
dominated by the diffusive processes both for the weak and strong stable
stratification ($\beta =2/3$). For the last case influence of the low boundary
can overcome the wave effects and result in $\beta =1/2$ for the vertical
component of the velocity field (the spontaneous breaking of the space
translational symmetry - homogeneity). For the unstably stratified turbulence
in the Rayleigh-Taylor mixing zone the diffusive processes ($\beta =2/3$) are
the most common dominating processes in the anisotropic chaotic mixing of the
two fluids under buoyancy forces. The distributed chaos in Rayleigh-B\'{e}nard
turbulent convection in an upright cell is determined by the strong confinement
conditions. That is: the spontaneous breaking of the space translational
symmetry (homogeneity) by the finite boundaries ($\beta = 1/2$) or by the
non-perfect orientation of the cell along the buoyancy direction ($\beta
=4/7$). In all types of turbulence appearance of an inertial range of scales
results in deformation of the distributed chaos and $\beta =3/5$.
