There is a difference between solubility and acidity. Acetate is easily dissolved, or solvated, by a variety of polar solvents. This has to do with acetate, or sodium acetate as it is normally stored, being a charged molecule, which is highly conducive to solvation by a polar solvent. This is what is meant by acetate being "highly soluble."
Acetic acid is readily dissolved as well. On the other hand, for acetic acid to dissociate to acetate and a proton, is not so favorable. This corresponds to the weak Ka of acetic acid. It is a weak acid.
Ksp is a measure of dissociation, but it is a term reserved generally for solids, while Ka is the term used for acids. They both mean the same thing - the dissociation of the molecule - but a distinction between the two is made because acids can be soluble in a medium without any indication as to how favorable their dissociation is. I should say, Ksp is used with solids always in the context of solubility, while Ka is used in the context of how well the molecule functions as an acid, and not in regard to the molecules solubility. The K is merely an expression for an equilibrium. Subscripts like sp, a, b, P, etc. provide the context.
I hope that helps, and I hope I am right. If someone else wants to correct me, please do!