  We illustrate that regular black holes and horizonless stars, typically
considered as quite distinct families of black hole mimickers, are intimately
intertwined. We show that any spherically symmetric regular black hole can be
continuously deformed into a horizonless star under the mild conditions of
non-negativity of gravitational energy (Misner--Sharp quasi-local mass), and an
assumed linear relation between the latter and the Arnowitt--Deser--Misner
(ADM) mass. We illustrate this general result by considering the family of
geometries proposed by Hayward as the description of regular black holes, and
we also describe the properties of the corresponding horizonless stars. The
form of the associated effective stress-energy tensor shows that these
horizonless stars can be identified as anisotropic gravastars with a soft
surface and inner/outer light rings. We also construct dynamical geometries
that could describe the evolution of regular black holes towards horizonless
stars, and show that semiclassical physics contains the necessary ingredients
to trigger the early stages of such dynamical evolution.
