  For static reductions of isotropic and anisotropic Magnetohydrodynamics
plasma equilibrium models, a complete classification of admitted point
symmetries and conservation laws up to first order is presented. It is shown
that the symmetry algebra for the isotropic equations is finite-dimensional,
whereas anisotropic equations admit infinite symmetries depending on a free
function defined on the set of magnetic surfaces. A direct transformation is
established between isotropic and anisotropic equations, which provides an
efficient way of constructing new exact anisotropic solutions. In particular,
axially and helically symmetric anisotropic plasma equilibria arise from
classical Grad-Shafranov and JFKO equations.
