The above is correct. I would add though that virtually all cameras have limited numbers of autofocus points, so if you try to shoot a small bird with a FF camera, you might not have enough AF points on it to do a good job. Whereas a crop-frame camera may have more AF points on the bird and thus do a better job of tracking it. That's part of the reason why crop frame cameras are popular among birders. There are other reasons as well, including cost and more frames per second per dollar (in some cases).
Not sure if it matters, but I only use the center point really