  We study wo distinct theta-exact Seiberg-Witten (SW) map expansions, (I) and
(II) respectively, up to the e3 order for the gauge parameter, gauge field and
the gauge field strengths of the noncommutative U*(1) gauge theory on the Moyal
space. We derive explicitly the closed form expression for the SW map ambiguity
between the two and observe the emergence of several new totally commutative
generalized star products. We also identify the additional gauge freedoms
within each of the e3 order field strength expansions and define corresponding
sets of deformation/ratio/weight parameters, (kappa,kappa_i) and
(kappa,kappa'_i), for these two SW maps respectively.
