In displacement reaction, more reactive element displaces the less reactive element from its compound. For example
Zn (s) + CuSO4 (aq)→ZnSO4(aq)+Cu(s)
But in double displacement reaction, mutual exchange of ions takes place. For example
HCl (aq) + AgNO3 (aq)→ AgCl (s) + HNO3 (aq)