The difference is that one involves simple dissolving of a solid into water and the other involves an actual chemical reaction. Copper sulfate (CuSO4) is an ionic salt that will dissolve in water whether acid is present or not. The presence of the HCl in the water will probably help to increase the rate of dissolving since the sulfate anion will react with protons to produce carbonic acid which immediately breaks down into water and carbon dioxide. Zinc, on the other hand, will do absolutely nothing in plain water. In dilute HCl, the zinc will react with the acid to produce zinc chloride and hydrogen gas. The zinc is oxidized while the protons are reduced. The equation is written below:
Zn + 2HCl --> H2 + ZnCl2
The solid zinc is slowly consumed and the zinc chloride is dissolved in water while the hydrogen bubbles out of solution. So the real difference here is the copper sulfate simply dissolves in the water while the zinc actually reacts with the acid.
Thank you a tonne!