  In the Minimal Supersymmetric Model (MSSM) and the Next to Minimal
Supersymmetric Model [(M+1)SSM], an upper bound on the lightest higgs mass can
be calculated. On the other hand, vacuum stability implies a lower limit on the
mass of the higgs boson in the Standard Model (SM). We find that a gap exists
for $m_t \stackrel{>}{\sim} 165$ GeV between the SM and both the MSSM and the
(M+1)SSM bounds. Thus, if the new top quark mass measurement by CDF remains
valid, a first measurement of the higgs mass will serve to exclude either the
SM or the MSSM/(M+1)SSM higgs sectors. In addition, we discuss Supersymmetric
Grand Unified Theories, other extentions of the SM, the discovery potential of
the lightest higgs, and the assumptions on which our conclusions are based.
