An anonymous function is just a function that has no name.
A closure is a function that captures the state of the surrounding environment.

An anonymous function does not necessarily need to create a closure, and a closure is not created only for anonymous functions.

anonymous function:

(function() { // anonymous function
	// code to run
})();

closure:

function outer() {
    var greeting = "hello ";

    (function(name, greeting) {
        alert(greeting + name);
    })("John Doe", greeting);
}