  We present a case study for the doubly charged Higgs bosons $H^{\pm\pm}$ pair
production in $e^+e^-$ and $pp$ colliders with their subsequent decays to four
charged leptons. We consider the Higgs Triplet Model (HTM) not restricted by
the custodial symmetry and the Minimal Left-Right Symmetric Model (MLRSM). The
models include scalar triplets with different complexity of scalar potentials
and, due to experimental restrictions, completely different scales of
non-standard triplet vacuum expectation values. In both models, a doubly
charged Higgs boson $H^{\pm\pm}$ can acquire a mass of hundreds of
gigaelectronvolts, which can be probed at HL-LHC, future $e^+e^-$, and hadron
colliders. We take into account a comprehensive set of constraints on the
parameters of both models coming from neutrino oscillations, LHC, $e^+e^-$ and
low-energy lepton flavour violating data and assume the same mass of
$H^{\pm\pm}$. Our finding is that the $H^{\pm\pm}$ pair production in lepton
and hadron colliders is comparable in both models, though more pronounced in
MLRSM. We show that the decay branching ratios can be different within both
models, leading to distinguishable four lepton signals and that the strongest
are $4\mu$ events yielded by MLRSM. Typically we find that MLRSM signals are
one order of magnitude larger that in HTM. For example, the $pp \to 4\mu$ MLRSM
signal for 1 TeV $H^{\pm \pm}$ mass results in a clearly detectable
significance of $S \simeq 11$ for HL-LHC and $S \simeq 290$ for FCC-hh. Finally
we provide quantitative predictions for the dilepton invariant mass
distributions and lepton separations which help to identify non-standard
signals.
