Hydrates In Aqueous Solutions
Yes, the ‘hydrate’ label applies exclusively to solids. Consider the following experiment: Dissolve both anhydrous $\ce{CuSO4}$ and $\ce{CuSO4 . 5 H2O}$ in water. You will get the same, blue solution.

What happened on a microscopic level is that the crystal lattice which once included the water atoms is broken up and the ions dissolve separately. What used to be copper(II) sulphate pentahydrate is now turned into a hexaaquacopper(II) complex.

$$\ce{CuSO4.5 H2O + H2O -&gt; [Cu(H2O)6]^2+ + SO4^{2-}_{~(aq)}}$$