What does it mean to say that a strong base is only slightly soluble? I've often seen the hydroxides of Calcium, Strontium and Barium described as "strong bases that are only slightly soluble," or similar.  But strong bases dissociate completely in solution, so I would guess this means that such hydroxides dissolve only a small amount, but the dissolved portion dissociates completely.

But the problem with this interpretation is that these hydroxides are ionic compounds, and my understanding is that "dissolve" is essentially equivalent to "dissociate" for ionic compounds, i.e. ionic compounds dissolve by dissociating.

If there's no distinction between dissolving and dissociating for ionic compounds, what does the description "strong base that is only slightly soluble" mean?  How does it differ from the term "weak base?"

If there is a distinction, and it is possible for ionic compounds to dissolve without dissociating, how does such dissolution work?  I have a model for the distinction between dissolution and dissociation of covalent compounds: first the compound dissolves into separate molecules, then each molecule dissociates into two or more ions.  If ionic compounds can dissolve without dissociating, into what sort of particles do they dissolve? Formula units? Small clusters of ions?  Something else?
Solubility is different from dissolution, which is itself different from dissociation.

Solubility tells you the extent to which a substance dissolves. Dissolution is the kinetic process of solvation, when solvent molecules interact with solute molecules or ions. Dissociation is, from IUPAC, 


  
  The separation of a molecular entity into two or more molecular entities (or any similar separation within a polyatomic molecular entity). Examples include unimolecular heterolysis and homolysis, and the separation of the constituents of an ion pair into free ions.
  The separation of the constituents of any aggregate of molecular entities.
  


Dissociation is the mode of solvation for ionic compounds.



I think your confusion stems from associating solubility and dissolution improperly. ChemGuide directly answers your question here:


  Some strong bases like calcium hydroxide aren't very soluble in water. That doesn't matter - what does dissolve is still 100% ionised into calcium ions and hydroxide ions. Calcium hydroxide still counts as a strong base because of that 100% ionisation.