With this code...
if (listText == displayArraysString)
{
MessageBox.Show("Found a match!");
}
you are asking "Is the listText control the same control as displayArraysString" and that answer to that is "false" and always will be as they refer to different instances on textboxes.
This code...
if (listText.Text == displayArraysString.Text)
{
MessageBox.Show("Found a match!");
}
is asking "Is the text in listText the same as the text in displayArraysString" which is what you really want to know.