How to associate one TextBox with other TextBox?

You should remember that your textBox_TextChanged is an instance, not a static function. That said, in addition to the two parameter you use, it also has hidden "this" parameter. In what class this method is declared? Use this instance to pass a reference to another control. For example, imaging this is a form (very likely), and your UI is System.Windows.Forms. I also don't want to use a named handler, it looks ugly. So, let's see:

partial public class MyForm { // MyForm : System.Windows.Forms.Form is specified in some other part of "partial", typically generated from template
   TextBox OneTextBox = //...
   TextBox AnotherTextBox = //...

   public MyForm() {
       OneTextBox.TextChanged += (sender, eventArgs) => { //types of sender, eventArgs are inferred by a compiler from known event type
           TextBox thisTextBox = (TextBox)sender; // this cast cannot fail, this is how controls invoke events
           // at this time, thisTextBox == OneTextBox; but you could use OneTextBox directly, because this is actually passed with "this":
           thisTextBox = this.OneTextBox;
           // or just
           thisTextBox = OneTextBox; // because there is no ambiguity
           // and finally, drums...:
           TextBox anotherTextBox = this.AnotherTextBox; // another totally redundant declaration and "this.", just for explanation
           // use AnotherTextBox, which is this.AnotherTextBox
       };
   }
}

Of the text boxes are in different forms, the difference is minor: you need somehow pass a reference to AnotherTextBox to another form. This is reduced to the popular question about form collaboration. The most robust solution is implementation of an appropriate interface in form class and passing the interface reference instead of reference to a "whole instance" of a Form. Please see my past solution for more detail: How to copy all the items between listboxes in two forms[^].

Please also see other solutions in this discussion. If the application is simple enough, the solution could be as simple as declaring of some internal property in one form and passing a reference to the instance of one form to the instance of another form. For more complex projects, such violation of strictly encapsulated style and loose coupling could add up the the accidental complexity of the code and invite mistakes, so the well-encapsulated solution would be preferable.

Please see also:
http://en.wikipedia.org/wiki/Accidental_complexity[^],
http://en.wikipedia.org/wiki/Loose_coupling[^].

—SA