  We study the evolution of the superconducting coherence length $\xi_0$ from
weak to strong coupling, both within a s-wave and a d-wave lattice model. We
show that the identification of $\xi_0$ with the Cooper-pair size $\xi_{pair}$
in the weak-coupling regime is meaningful only for a fully-gapped (e.g.,
s-wave) superconductor. Instead in the d-wave superconductor, where
$\xi_{pair}$ diverges, we show that $\xi_0$ is properly defined as the
characteristic length scale for the correlation function of the modulus of the
superconducting order parameter. The strong-coupling regime is quite
intriguing, since the interplay between particle-particle and particle-hole
channel is no more negligible. In the case of s-wave pairing, which allows for
an analytical treatment, we show that $\xi_0$ is of order of the lattice
spacing at finite densities. In the diluted regime $\xi_0$ diverges, recovering
the behavior of the coherence length of a weakly interacting effective bosonic
system. Similar results are expected to hold for d-wave superconductors.
