  We search for features in the mass distribution of detected compact binary
coalescences which signify the transition between neutron stars and black
holes. We analyze all gravitational wave detections by LIGO-Virgo-KAGRA made
through the end of the first half of the third observing run, and find clear
evidence for two different populations of compact objects based solely on
gravitational wave data. We confidently (99.3%) find a steepening relative to a
single power law describing neutron stars and low-mass black holes below
$2.4^{+0.5}_{-0.5}\text{ M}_{\odot}$, which is consistent with many predictions
for the maximum neutron star mass. We find suggestions of the purported lower
mass gap between the most massive neutron stars and the least massive black
holes, but are unable to conclusively resolve it with current data. If it
exists, we find the lower mass gap's edges to lie at $2.2^{+0.7}_{-0.5}\text{
M}_{\odot}$ and $6.0^{+2.4}_{-1.4}\text{ M}_{\odot}$. We re-examine events that
have been deemed "exceptional" by the LIGO-Virgo-KAGRA collaborations in the
context of these features. We analyze GW190814 self-consistently in the context
of the full population of compact binaries, finding support for its secondary
to be either a neutron star or a lower mass gap object, consistent with
previous claims. Our models are the first to accommodate this event, which is
an outlier with respect to the binary black hole population. We find that
GW200105 and GW200115 probe the edges of, and may have components within, the
lower mass gap. As future data improve global population models, the
classification of these events will also improve.
