When bowling a leg break, the seam is usually under all of the fingers, i.e. the fingers run over the ball and right before release an anticlockwise spin is exerted that causes the ball to turn from the right to the left (as seen by a right arm leg break bowler) after pitching. During this process, the wrist is usually moved to the left (of a right arm bowler).
A googly is a unique delivery bowled with a similar action, except that the wrist comes down straight. This causes a clockwise spin on the ball, something that can also be achieved by spinning the ball further than a usual leg break right before release with the help of the fingers.
An off break, as you have pointed out, doesn't quite involve the use of the wrist but rather the fingers that exert a clockwise spin on the ball. So to answer your question, a googly is not an off break but rather a special delivery used quite effectively by seasoned leg break bowlers.
Yes, it's a curious combination of both.
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