  In the present paper, we consider two different {\em Finsler} structures $L$
and $L^*$ on the same base manifold $M$, with no relation preassumed between
them. \par Introducing the $\pi$-tensor field representing the difference
between the Cartan connections associated with $L$ and $L^*$, we investigate
the conditions, to be satisfied by this $\pi$-tensor field, for the geometric
objects associated with $L$ and $L^*$ to have the same properties. Among the
items investigated in the paper, we consider the properties of being a
geodesic, a Jacobi field, a Berwald manifold, a locally Minkowskian manifold
and a Landsberg manifold. \par It should be noticed that our approach is
intrinsic, i.e., it does not make use of local coordinate techniques.
