  Topological phases of matter are distinguished by topological invariants,
such as Chern numbers and topological spins, that quantize their response to
electromagnetic currents and changes of ambient geometry. Intriguingly, in the
$\nu=2/5$ fractional quantum Hall effect, prominent theoretical approaches --
the composite fermion theory and conformal field theory -- have constructed two
distinct states, the Jain composite fermion (CF) state and the Gaffnian state,
for which many of the topological indices coincide and even the microscopic
ground state wave functions have high overlap with each other in system sizes
accessible to numerics. At the same time, some aspects of these states are
expected to be very different, e.g., their elementary excitations should have
either Abelian (CF) or non-Abelian (Gaffnian) statistics. In this paper we
investigate the close relationship between these two states by considering not
only their ground states, but also the low-energy charged excitations. We show
that the low-energy physics of both phases is spanned by the same type of
quasielectrons of the neighbouring Laughlin phase. The main difference between
the two states arises due to an implicit assumption of short-range interaction
in the CF approach, which causes a large splitting of the variational energies
of the Gaffnian excitations. We thus propose that the Jain phase emerges as an
effective Abelian low-energy description of the Gaffnian phase when the
Hamiltonian is dominated by two-body interactions of sufficiently short range.
