  The convex cone $SC_{\mathrm{SLip}}^1(\mathcal{X})$ of real-valued smooth
semi-Lipschitz functions on a Finsler manifold $\mathcal{X}$ is an
order-algebraic structure that captures both the differentiable and the
quasi-metric feature of $\mathcal{X}$. In this work we show that the subset of
smooth semi-Lipschitz functions of constant strictly less than $1$, denoted
$SC_{1^{-}}^1(\mathcal{X})$, can be used to classify Finsler manifolds and to
characterize almost isometries between them, in the lines of the classical
Banach-Stone and Mykers-Nakai theorems.
