  Binary neutron-star mergers and heavy-ion collisions are related through the
properties of the hot and dense nuclear matter formed during these extreme
events. In particular, low-energy heavy-ion collisions offer exciting prospects
to recreate such {extreme} conditions in the laboratory. However, it remains
unexplored to what degree those collisions can actually reproduce hot and dense
matter formed in binary neutron star mergers. As a way to understand
similarities and differences between these systems, we {discuss their geometry
and }perform a direct numerical comparison of the thermodynamic conditions
probed in both collisions. To enable a direct comparison, we employ a
finite-temperature equation of state able to describe the entire high-energy
phase diagram of Quantum Chromodynamics. Putting side by side the evolution of
both systems, we find that laboratory heavy-ion collisions at the energy range
of $E_{\mathrm{lab}}=0.4 - 0.6\ A$ MeV probe (thermodynamic) states of matter
that are very similar to those created in binary neutron-star mergers. These
results can inform future low-energy heavy-ion collisions probing this regime.
