Stochastic exponential is
$\mathcal{E}_t(X)=e^{X_t-\frac{1}{2}<X^c>_t}\prod_{s\leq t}(1+\Delta X_t)e^{-\Delta X_s}$
and usual exponential is $e^{X_t}$
I guess, if process is continuous and of finite variation then it they should be the same, right? any weaker conditions?