  In this paper, the main aim is to give some characterizations of the
boundedness of the maximal or nonlinear commutator of the $p$-adic fractional
maximal operator $ \mathcal{M}_{\alpha}^{p}$ with the symbols belong to the
$p$-adic Lipschitz spaces in the context of the $p$-adic version of variable
Lebesgue spaces, by which some new characterizations of the Lipschitz spaces
and nonnegative Lipschitz functions are obtained in the $p$-adic field context.
Meanwhile, Some equivalent relations between the $p$-adic Lipschitz norm and
the $p$-adic variable Lebesgue norm are also given.
