While it may be true that mass is a form of energy, it is not the case
that all forms of energy are mass. For instance, the kinetic energy
associated with an object's total momentum (i.e. the kinetic energy of
the motion of the object's center of mass) is *not* a mass. Likewise,
photons have energy, but they don't have mass. So mass and energy are
not really equivalent concepts. However, you could say that the mass of
an of an object is its *internal* energy, or its energy as observed in a
frame for which its instantaneous total momentum vanishes.
(Note that the definition of 'mass' use here is the normal modern usage
of the term as by practicing physicists as the invariant timelike
magnitude of the object's energy-momentum 4-vector (1-form), and, most
definitely, does *not* mean the so-called 'relativistic mass'.)