  We present the identification of 634 variable stars in the Milky Way dSph
satellite Sculptor based on archival ground-based optical observations spanning
$\sim$24 years and covering $\sim$ 2.5 deg$^2$. We employed the same
methodologies as the "Homogeneous Photometry" series published by Stetson. In
particular, we have identified and characterized one of the largest (536) RR
Lyrae samples so far in a Milky Way dSph satellite. We have also detected four
Anomalous Cepheids, 23 SX Phoenicis stars, five eclipsing binaries, three field
variable stars, three peculiar variable stars located above the horizontal
branch - near to the locus of BL Herculis - that we are unable to classify
properly. Additionally we identify 37 Long Period Variables plus 23 probable
variable stars, for which the current data do not allow us to determine the
period. We report positions and finding charts for all the variable stars, and
basic properties (period, amplitude, mean magnitude) and light curves for 574
of them. We discuss the properties of the RR Lyrae stars in the Bailey diagram,
which supports the coexistence of subpopulations with different chemical
compositions. We estimate the mean mass of Anomalous Cepheids
($\sim$1.5M$_{\odot}$) and SX Phoenicis stars ($\sim$1M$_{\odot}$). We discuss
in detail the nature of the former. The connections between the properties of
the different families of variable stars are discussed in the context of the
star formation history of the Sculptor dSph galaxy.
