  The wave-front set for an irreducible admissible representation of a $p$-adic
reductive group is the set of maximal nilpotent orbits which appear in the
local character expansion. By M\oe glin-Waldspurger, they are also the maximal
nilpotent orbits whose associated degenerate Whittaker models are non-zero.
However, in the literature there are two versions commonly used, one defining
maximality using analytic closure and the other using Zariski closure. We show
that these two definitions are non-equivalent for $G=Sp_4$.
