How can I tell if a form is closed from the controlbox (system menu) or from a call to Form.Close

One way to do this is to override the form’s WndProc method and check for WM_SYSCOMMAND and SC_CLOSE. Looking for WM_CLOSE in the override is not sufficient as WM_CLOSE is seen in both cases. A sample is available for download (C#, VB).

public const int SC_CLOSE = 0xF060;
public const int WM_SYSCOMMAND = 0x0112;

//_closeClick is a bool member of the form initially set false...
// It can be tested in the Closing event to see how the closing came about.
  
protected override void WndProc(ref System.Windows.Forms.Message m)
{
  if(m.Msg == WM_SYSCOMMAND && (int)m.WParam == SC_CLOSE)
    this._closeClick = true;

  base.WndProc(ref m);
}