<!--td {border: 1px solid #ccc;}br {mso-data-placement:same-cell;}-->
A displacement reaction is the one when a more reactive substance displaces a less reactive one from its salt solution whereas a double displacement reaction is the one where a mutual exchange of ions happens between two compounds.
In a displacement reaction, only a single displacement takes place whereas in the double displacement reaction, as the name suggests two displacement takes place between the molecules.
Example:
Displacement reaction: Mg(s)+2HCl(aq)→MgCl2(aq)+H2(g)
Double displacement reaction:
2KBr(aq)+BaI2(aq)→2KI(aq)+BaBr2(s)