Ionisation vs Dissociation
The parameter a in front of √C is empirical. It varies from solute to solute.
And yes, the dissociation is complete at infinite dilution.
Dissociation is the separation of ions when dissolving a salt in water. If NaCl is dissociated, it yields two independent ions, one Na+ and one Cl−
Ionization is what happens when an atom or a molecule looses one electron, without being modified or broken. If $\ce{NaCl}$ is dissociated, it gives two independent ions, one $\ce{Na+}$ and one $\ce{Cl−}$
If $\ce{H2O}$ is ionized, it gives an ion $\ce{H2O}$+ and one electron, but the atoms of the molecule are not separated from one another.