They're actually really similar. How you call them is exactly the same.The difference lies in how the browser loads them into the execution context.

Function declarations load before any code is executed.

Function expressions load only when the interpreter reaches that line of code.

So if you try to call a function expression before it's loaded, you'll get an error! If you call a function declaration instead, it'll always work, because no code can be called until all declarations are loaded.

Example: Function Expression

alert(foo()); // ERROR! foo wasn't loaded yet
var foo = function() { return 5; } 

Example: Function Declaration

alert(foo()); // Alerts 5. Declarations are loaded before any code can run.
function foo() { return 5; } 

As for the second part of your question:

var foo = function foo() { return 5; } is really the same as the other two. It's just that this line of code used to cause an error in safari, though it no longer does.

Along with that very good answer, the only advantage I can see is dynamically changing a function call.

For example this code :

function foo(){
    console.log('foo');
}

function bar(){
    console.log('bar');
}

var myFn = foo;

myFn();

setInterval(function(){
    if(myFn === foo) myFn = bar;
    else myFn = foo;
}, 5000);

setInterval(function(){
    myFn()
}, 6000);

It will never log the same thing since you reassign a global variable, every innerscope function will change while this code :

function foo(){
    console.log('foo');
}

setInterval(function(){
    function foo(){
        console.log('Changed foo');
    }

    foo()
}, 5000)

setInterval(function(){
    foo()
}, 5000)

Will log 2 different things. You can only change the current scope function, not the global.