  Charge-order stripes of different types occur when copper oxides are doped
with either heterovalent metal, like $La_{2-x}Sr_xCuO_4$, or oxygen, like
$YBa_2Cu_3O_{6+y}$. The difference shows up in the doping dependence of their
incommensurability: $q_c(x) \propto \sqrt{x-\check{p}}$ but $q_c(y) \approx
0.3$. The square-root dependence in the former compound family results from
Coulomb repulsion between doped holes (or electrons), residing pairwise in
lattice-site $O$ (or $Cu$) atoms of the $CuO_2$ planes. The almost constant
$q_c(y)$ value in the second family results from the aggregation of ozone-like
molecules, formed from $O^{2-}$ ions of the host with embedded oxygen atoms,
$O_i$, at interstitial sites in the $CuO_2$ planes. The magnetic moments,
$\mathbf{m}(O)$, of the lattice-defect $O$ atoms in the first family arrange
antiferromagnetically, which gives rise to accompanying magnetization stripes
of incommensurability $q_m(x) = q_c(x)/2$. The ozone complexes have a vanishing
magnetic moment, $\mathbf{m}=0$, which explains the absence of accompanying
magnetization stripes in the second family. Embedding excess oxygen as $O_i$
atoms in $CuO_2$ planes is likewise assumed for $HgBa_2CuO_{4+\delta}$ and
oxygen-enriched bismuth cuprates. A combination of characteristics from both
families is present in oxygen-enriched $La_2CuO_{4+y}$. The validity of
determining the hole density in oxygen-enriched cuprates with the
universal-dome method is independently confirmed. Besides causing different
types of stripes, the two types of lattice-defect oxygen may also cause
different types of superconductivity. This could explain the much higher
$T_{c,max}$ in oxygen-enriched than $Sr$-doped cuprates, as well as the cusped
cooling-curves of X-ray intensity diffracted by stripes in the former family.
