  The semiclassical limit of full non-commutative gauge theory is known as
Poisson gauge theory. In this work we revise the construction of Poisson gauge
theory paying attention to the geometric meaning of the structures involved and
advance in the direction of a further development of the proposed formalism,
including the derivation of Noether identities and conservation of currents.
For any linear non-commutativity, $\Theta^{ab}(x)=f^{ab}_c\,x^c$, with
$f^{ab}_c$ being structure constants of a Lie algebra, an explicit form of the
gauge Lagrangian is proposed. In particular a universal solution for the matrix
$\rho$ defining the field strength and the covariant derivative is found. The
previously known examples of $\kappa$-Minkowski, $\lambda$-Minkowski and
rotationally invariant non-commutativity are recovered from the general
formula. The arbitrariness in the construction of Poisson gauge models is
addressed in terms of Seiberg-Witten maps, i.e., invertible field redefinitions
mapping gauge orbits onto gauge orbits.
