  Many astrophysical small-scale dynamos (SSDs) amplify weak magnetic fields
via highly compressible, supersonic turbulence, but established SSD theories
have overlooked these compressible effects. To address this, we perform
visco-resistive SSD simulations across a range of sonic Mach numbers
($\mathcal{M}$), hydrodynamic Reynolds numbers ($\mathrm{Re}$), and magnetic
Prandtl numbers ($\mathrm{Pm}$). We develop robust methods to measure kinetic
and magnetic energy dissipation scales ($\ell_\nu$ and $\ell_\eta$) and the
scale of strongest magnetic fields ($\ell_\mathrm{p}$) during the kinematic
phase. We demonstrate that $\ell_\nu/\ell_\eta \sim \mathrm{Pm}^{1/2}$ is a
universal feature for $\mathrm{Pm} \geq 1$ SSDs, regardless of $\mathcal{M}$ or
$\mathrm{Re}$. Incompressible SSDs (either $\mathcal{M} \leq 1$ or $\mathrm{Re}
< \mathrm{Re}\mathrm{crit} \approx 100$) concentrate magnetic energy at
$\ell_\mathrm{p} \sim \ell_\eta$ with inversely correlated field strength and
curvature. However, for compressible SSDs ($\mathcal{M} > 1$ and $\mathrm{Re} >
\mathrm{Re}\mathrm{crit}$), shocks concentrate magnetic energy in large
structures with $\ell_\mathrm{p} \sim (\ell_\mathrm{turb} /
\ell_\mathrm{shock})^{1/3} \ell_\eta \gg \ell_\eta$, where
$\ell_\mathrm{shock}$ is the characteristic shock width, and
$\ell_\mathrm{turb}$ is the outer scale of the turbulent field. In this regime,
magnetic field-line curvature becomes nearly independent of field strength.
These results have implications for galaxy mergers and cosmic ray transport
models in the interstellar medium.
