Miter is the American spelling of mitre. British English writes mitre; the word is the same. It has two lives that do not feel related until you look at the shape. First, a miter is the tall, pointed hat a bishop wears in church — two peaks, front and back. Second, in building and woodwork, a miter is a corner joint where two pieces are cut at an angle, often 45 degrees, so they meet neatly, as in a picture frame. You can also use it as a verb: to miter the corners. If you see miter on an American tool (“miter saw”), it is the woodworking sense. It is not a different word from mitre, and it is not “mightier” or “meter.”