  We compare primordial black hole (PBH) constraints on the power spectrum and
mass distributions using the traditional Press Schechter formalism, peaks
theory, and a recently developed version of peaks theory relevant to PBHs. We
show that, provided the PBH formation criteria and the power spectrum smoothing
are treated consistently, the constraints only vary by $\sim$10\% between
methods (a difference that will become increasingly important with better
data). Our robust constraints from PBHs take into account the effects of
critical collapse, the non-linear relation between $\zeta$ and $\delta$, and
the shift from the PBH mass to the power spectrum peak scale. We show that
these constraints are remarkably similar to the pulsar timing array (PTA)
constraints impacting the black hole masses detected by the LIGO and Virgo, but
that the $\mu$-distortion constraints rule out supermassive black hole (SMBH)
formation and potentially even the much lighter mass range of $\sim$(1-100)
$\mathrm{M}_\odot$ that LIGO/Virgo probes.
