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The first one (function doSomething(x)) should be part of an object notation.

The second one (var doSomething = function(x){ alert(x);}) is simply creating an anonymous function and assigning it to a variable, doSomething. So doSomething() will call the function.

You may want to know what a function declaration and function expression is.

A function declaration defines a named function variable without requiring variable assignment. Function declarations occur as standalone constructs and cannot be nested within non-function blocks.

function foo() {
 return 3;
}

ECMA 5 (13.0) defines the syntax as
function Identifier ( FormalParameterList_opt ) { FunctionBody }

In above condition the function name is visible within its scope and the scope of its parent (otherwise it would be unreachable).

And in a function expression

A function expression defines a function as a part of a larger expression syntax (typically a variable assignment ). Functions defined via functions expressions can be named or anonymous. Function expressions should not start with "function".

// Anonymous function expression
var a = function() {
 return 3;
}
// Named function expression
var a = function foo() {
 return 3;
}
// Self-invoking function expression
(function foo() {
 alert("hello!");
})();

ECMA 5 (13.0) defines the syntax as
function Identifier_opt ( FormalParameterList_opt ) { FunctionBody }