  We report growth characteristics of epitaxial $\beta$-Na$_{0.6}$CoO$_{2}$ and
$\gamma$-Na$_{0.7}$CoO$_{2}$ thin films on (001) sapphire substrates grown by
pulsed-laser deposition. Reduction of deposition rate could change structure of
Na$_{x}$CoO$_{2}$ thin film from $\beta$-phase with island growth mode to
$\gamma$-phase with layer-by-layer growth mode. The
$\gamma$-Na$_{0.7}$CoO$_{2}$ thin film exhibits spiral surface growth with
multiterraced islands and highly crystallized texture compared to that of the
$\beta$-Na$_{0.6}$CoO$_{2}$ thin film. This heterogeneous epitaxial film growth
can give opportunity of strain effect of physical properties and growth
dynamics of Na$_{x}$CoO$_{2}$ as well as subtle nature of structural change.
