  Star clusters are known to have smaller intrinsic metallicity spreads than
dwarf galaxies due to their shorter star formation timescales. Here we use
individual spectroscopic [Fe/H] measurements of stars in 19 Local Group dwarf
galaxies, 13 Galactic open clusters, and 49 globular clusters to show that star
cluster and dwarf galaxy linear metallicity distributions are binomial in form,
with all objects showing strong correlations between their mean linear
metallicity $\bar{Z}$ and intrinsic spread in metallicity $\sigma(Z)^{2}$. A
plot of $\sigma(Z)^{2}$ versus $\bar{Z}$ shows that the correlated
relationships are offset for the dwarf galaxies from the star clusters. The
common binomial nature of these linear metallicity distributions can be
explained with a simple inhomogeneous chemical evolution model (e.g., Oey
2000), where the star cluster and dwarf galaxy behaviour in the
$\sigma(Z)^{2}-\bar{Z}$ diagram is reproduced in terms of the number of
enrichment events, covering fraction, and intrinsic size of the enriched
regions. The inhomogeneity of the self-enrichment sets the slope for the
observed dwarf galaxy $\sigma(Z)^{2}-\bar{Z}$ correlation. The offset of the
star cluster sequence from that of the dwarf galaxies is due to pre-enrichment,
and the slope of the star cluster sequence represents the remnant signature of
the self-enriched history of their host galaxies. The offset can be used to
separate star clusters from dwarf galaxies without a priori knowledge of their
luminosity or dynamical mass. The application of the inhomogeneous model to the
$\sigma(Z)^{2}-\bar{Z}$ relationship provides a numerical formalism to connect
the self-enrichment and pre-enrichment between star clusters and dwarf galaxies
using physically motivated chemical enrichment parameters.
