  The neutron skin thickness of nuclei is a sensitive probe of the nuclear
symmetry energy having multiple implications for nuclear and astrophysical
studies. However, precision measurements of this observable are difficult. The
analysis of the experimental data may imply some assumptions about the bulk or
surface nature of the formation of the neutron skin. Here, we study the bulk or
surface character of neutron skins of nuclei following from calculations with
Gogny, Skyrme, and covariant nuclear mean-field interactions. These
interactions are successful in describing nuclear charge radii and binding
energies but predict different values for neutron skins. We perform the study
by fitting two-parameter Fermi distributions to the calculated self-consistent
neutron and proton densities. We note that the equivalent sharp radius is a
more suitable reference quantity than the half-density radius parameter of the
Fermi distributions to discern between the bulk and surface contributions in
neutron skins. We present calculations for nuclei in the stability valley and
for the isotopic chains of Sn and Pb.
