  The noncommutative string theory is described by embedding open string theory
in a constant second rank antisymmetric $B_{\mu\nu}$ field and the
noncommutative gauge theory is defined by a deformed $\star$ product. As a
check, study of various scattering amplitudes in both noncommutative string and
noncommutative gauge theory confirm that in the $\alpha^{'}\to 0$ limit, the
noncommutative string theoretic amplitude goes over to the noncommutative gauge
theoretic amplitude, and the couplings are related as
$g_{YM}=G_0\sqrt{\frac{1}{2\alpha^{'}}}$. Furthermore we show that in this
limit there will not be any correction to the gauge theoretic action because of
absence of massive modes. We get sin/cos factors in the scattering amplitudes
depending on the odd/even number of external photons.
