WAMP: acronym for Windows Operating System, Apache(Web server), MySQL Database and PHP Language.
XAMPP: acronym for X (any Operating System), Apache (Web server), MySQL Database, PHP Language and PERL.
XAMPP and WampServer are both free packages of WAMP, with additional applications/tools, put together by different people.
Their differences are in the format/structure of the package, the configurations, and the included management applications.
In short: XAMPP supports more OSes and includes more features