  Motivated by searches for so-called leptonic scalars at the LHC and the
recent measurement of the $W$ boson's mass at the Tevatron, we revisit the
phenomenology of the Zee-Babu model for neutrino masses and the ability to
differentiate it from the Type II Seesaw model at the LHC. We conclude that
this task is much more difficult than previously believed. All inputs equal in
the two scenarios, we find that total and differential rates for producing
pairs of doubly and singly charged scalars are identical in shape and only
differ in normalization. The normalization is given by the ratio of hadronic
cross sections and can be unity. Differences in cross sections are small and
can be hidden by unknown branching rates. This holds for Drell-Yan,
$\gamma\gamma$ fusion, and $gg$ fusion, as well as observables at LO and NLO in
QCD. This likeness allows us to reinterpret Run II limits on the Type II Seesaw
and estimate projections for the HL-LHC. Using updated neutrino oscillation
data, we also find that some collider observables, e.g., lepton
flavor-violating branching ratios, are now sufficiently precise to provide a
path forward. Other means of discrimination are also discussed. As a byproduct
of this work, we report the availability of new Universal \texttt{FeynRules}
Object libraries, the \texttt{SM\_ZeeBabu} UFO, that enable fully differential
simulations up to NLO+LL(PS) with tool chains employing
\texttt{MadGraph5\_aMC@NLO}.
