There are two official GUI tookits for C#: WPF and WinForms. The second one is older and the only one available on Mono.
For WinForms, you're going to have the
TextChanged event on one TextBox modify the
Text property of the other one. Knowing how to do so is
fundamental to C# programming. There are many tutorials on how to set up the
events and
delegates needed to make this happen --- including one you can find by following the first link.