In this paper we report the theoretical and experimental characterization of a pulsed optically pumped vapor-cell frequency standard based on the detection of the free-induction decay microwave signal. The features that make this standard similar to a pulsed passive maser are presented. In order to predict and optimize the frequency stability, thermal and shot noise sources are analyzed, as well as the conversions of the laser and microwave fluctuations into the output frequency. The experimental results obtained with a clock prototype based on $^{87}\mathrm{Rb}$ in buffer gas are compared with the theoretical predictions, showing the practical possibility to implement a frequency standard limited in the medium term only by thermal drift. The achieved frequency stability is ${\ensuremath{\sigma}}_{y}(\ensuremath{\tau})=1.2\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}12}{\ensuremath{\tau}}^{\ensuremath{-}1∕2}$ for measurement times up to $\ensuremath{\tau}\ensuremath{\approx}{10}^{5}\phantom{\rule{0.3em}{0ex}}\mathrm{s}$. It represents one of the best results reported in literature for gas cell frequency standards and is compliant with the present day requirements for on board space applications.