Detailed Explanation of Variable Capture in Closures

Is tricky. Will come onto it in a minute.
There's no difference - in both cases, it's the variable itself which is captured.
Nope, no boxing occurs.

It's probably easiest to demonstrate how the capturing works via an example...

Here's some code using a lambda expression which captures a single variable:

using System;

class Test
{
    static void Main()
    {
        Action action = CreateShowAndIncrementAction();
        action();
        action();
    }

    static Action CreateShowAndIncrementAction()
    {
        Random rng = new Random();
        int counter = rng.Next(10);
        Console.WriteLine("Initial value for counter: {0}", counter);
        return () =>
        {
            Console.WriteLine(counter);
            counter++;
        };
    }
}

Now here's what the compiler's doing for you - except that it would use "unspeakable" names which couldn't really occur in C#.

using System;

class Test
{
    static void Main()
    {
        Action action = CreateShowAndIncrementAction();
        action();
        action();
    }

    static Action CreateShowAndIncrementAction()
    {
        ActionHelper helper = new ActionHelper();        
        Random rng = new Random();
        helper.counter = rng.Next(10);
        Console.WriteLine("Initial value for counter: {0}", helper.counter);

        // Converts method group to a delegate, whose target will be a
        // reference to the instance of ActionHelper
        return helper.DoAction;
    }

    class ActionHelper
    {
        // Just for simplicity, make it public. I don't know if the
        // C# compiler really does.
        public int counter;

        public void DoAction()
        {
            Console.WriteLine(counter);
            counter++;
        }
    }
}

If you capture variables declared in a loop, you'd end up with a new instance of ActionHelper for each iteration of the loop - so you'd effectively capture different "instances" of the variables.

It gets more complicated when you capture variables from different scopes... let me know if you really want that sort of level of detail, or you could just write some code, decompile it in Reflector and follow it through :)

Note how:

There's no boxing involved
There are no pointers involved, or any other unsafe code

EDIT: Here's an example of two delegates sharing a variable. One delegate shows the current value of counter, the other increments it:

using System;

class Program
{
    static void Main(string[] args)
    {
        var tuple = CreateShowAndIncrementActions();
        var show = tuple.Item1;
        var increment = tuple.Item2;

        show(); // Prints 0
        show(); // Still prints 0
        increment();
        show(); // Now prints 1
    }

    static Tuple<Action, Action> CreateShowAndIncrementActions()
    {
        int counter = 0;
        Action show = () => { Console.WriteLine(counter); };
        Action increment = () => { counter++; };
        return Tuple.Create(show, increment);
    }
}

... and the expansion:

using System;

class Program
{
    static void Main(string[] args)
    {
        var tuple = CreateShowAndIncrementActions();
        var show = tuple.Item1;
        var increment = tuple.Item2;

        show(); // Prints 0
        show(); // Still prints 0
        increment();
        show(); // Now prints 1
    }

    static Tuple<Action, Action> CreateShowAndIncrementActions()
    {
        ActionHelper helper = new ActionHelper();
        helper.counter = 0;
        Action show = helper.Show;
        Action increment = helper.Increment;
        return Tuple.Create(show, increment);
    }

    class ActionHelper
    {
        public int counter;

        public void Show()
        {
            Console.WriteLine(counter);
        }

        public void Increment()
        {
            counter++;
        }
    }
}

Detailed Explanation of Variable Capture in Closures

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