Water soluble molecules
This question really belongs at Chemistry.SE, but I'll give you a quick answer. A substance is soluble in water when its solid form (such as a sugar cube) completely dissolves in water to become a sugar solution. The sugar molecules themselves are unaffected, essentially - instead of all being bound to one another in a crystal, they are now floating around in the water. The proof is in the taste - solid sugar and sugar solutions taste pretty much the same. If the sugar had been broken down into component hydrogen, oxygen, and carbon, it would taste much different!

On the other hand, hydrolysis is what happens when water actually participates in a chemical reaction to break one or more molecular bonds within a certain molecule, breaking it down to two new molecules (or one molecule and an atom, or whatever). While sugar can be hydrolyzed, it requires either very high heat, or the presence of a catalyst such as an enzyme.