I think we are having a problem with terminology. Pull, swing, hinge, holding wood mean different things to different people. Just check out how many terms there are for just facecuts.
If the tree leans to the left of the lay, a thicker hinge (holding wood) on the right, will pull the tree toward the center. The facecut determines direction of fall, the hinge/holding wood is used to influence the stem's movement in relation to the facecut. This is a simple view of what can be a very complex piece of work.
It is tough to explain this with text, much easier at the base of a tree.
2Dogs is correct, Andy is too, so are some others. There just isn't one answer, although that won't stop the debate.