Decomposition reaction is different from displacement reaction however double decomposition and double displacement reactions are nearly same because the exchange of radicals and ions do not differ in these reactions.
In double displacement reaction is , the cations and anions are exchanged between the two reactants to produce two new products. This exchange occurs due to the more reactive metals which displace the other less reactive metal from its solution.
Ex: AgNO3 + NaCl -> NaNO3 + AgCl
Similarly, in double decomposition reaction,there is exchange of radicals between the two reacting species which decomposes to give new products as
AgNO3 + KCl -> KNO3 + AgCl