In the case of double displacement, they are the same thing.
Basically, it is more in the mechanism than the outcome. The single displacement only involves one set of elements or functional groups, not a matched pair.
A double displacement reaction, is a chemical process involving the exchange of bonds between two reacting chemical species, which results in the creation of products with similar or identical bonding affiliations.
In either case, it is really just a language issue, as both reactions involve a "displacement" (relocation) of several atoms or groups, and "decomposition" is any breakdown of a larger compound, even though in these cases the products are "recomposed" - regenerated in new forms.