Hammerhead (aka wingover) is a vertical reversal that yaws over near or at stall speed. (your pitch changes 90 degrees to enter the vert, 90 degrees to exit). This is a very limited maneuver. It is useful if you need to reverse in the vertical at slow speed with very little lateral displacement between your enterence and exit line. Specifically this is most often desired when you have an opponent in or near stall condition underneath you.
High Yo-Yo is an out of plane (geometricly) reversal, that is performed at nearly any speed. It does not have to go vertical. (your pitch changes to leave your original plane (approximately near horizontal), you roll up to 90 degrees, you reverse 180 with your pitch axis, you roll back to wings level, and change pitch to re-enter your original plane. If you take it to the extreme by going pure vertical, thats 360 degrees of pitch change to make a 180 heading change. No matter how out of plane your yo-yo ends up, it will still be more that 180 degrees of pitch changes.
Quoted from this thread "Vertical Turns"
"3 of these things are kind of the same"
An Immelman, a chandelle, and a pitchback have some commonalities. Each maneuver will gain over 100% of the distance of your turn radius in altitude from start to finish. All changes in your pitch axis during the maneuvers contribute toward your heading reversal (this is also true with flat turns and split-s). So they are all about making a 180 degree turn in a time and distance efficent manner.
The High Yo-Yo differs on these points. I gave the extreme example of a near 90 degree high yo-yo from hanger to hanger in the film to hilight the difference. In that film I make a 90 degree turn to exit the horizontal plane, a 180 degree heading reversal, and a 90 degree turn to re-enter the horizontal. That adds up to 360 degrees in pitch change, that is neither time effecient nor a short path. What it does accomplish is an exit to a desired position that would be impossible with an in plane turn.
This is often the same thing that you want to accomplish while in pursuit of a slower bogie. If you have low separation with the bogie and they break turn in front of you, any attempt at pure pursuit will likely result with you well outside of their turn, with enough room for them to turn into you. The combination of those to factors creates an overshoot. Instead, you use a high yo-yo to re-enter the bogies turning plane to a position where it is still possible to re-aquire his extended 6. Not only does it allow you a chance to get to your opponents extended 6 where you otherwise could not, but it also creates separation. So you are using that 'longer route' to manage your separation. All the while you are efficently transfering energy states to gain the performance you are looking for.
I should add that typically, a high yo-yo will be more in the range of 30-60 degrees out of plane, and how hard of a yo-yo you will want will depend both on the position you are trying to exit at, and the separation you can afford to allow. And I think I will leave it at that because of how well the high yo-yo has been covered in this discussion
As you can see the high yo-yo has a much different set of objectives than the other turns discussed. This is also a reason I have wanted to stack these maneuvers together in the same discussion. They all have similarities in the way they look, but they do have different properties, and differ slightly in what they are trying to achieve. Hopefully this will cut down any confusion on what is or isn't a high yo-yo, and give you a few lessor discussed maneuvers to work with.