  We apply the Darmois and the $C^3$ matching conditions to three different
spherically symmetric spacetimes. The exterior spacetime is described by the
Schwarzschild vacuum solution whereas for the interior counterpart we choose
different perfect fluid solutions with the same symmetry. We show that Darmois
matching conditions are satisfied in all three cases whereas the $C^3$
conditions are not fulfilled. We argue that this difference is due to a
non-physical behavior of the pressure on the matching surface.
