A more reactive metal can displace a less reactive metal from its salt solution, but a less reactive metal cannot displace a more reactive metal from its salt solution.
According to the reactivity series, copper is less reactive than zinc. Thus copper cannot displace zinc from its salt solution, but zinc can displace copper from its salt solution.
Copper + Zinc sulphate → No reaction
Zinc + Copper sulphate → Copper + Zinc sulphate