My projector has a Vertical Lens Shift where one can manually move the picture a large range, up to 100% of screen height. It also has a Vertical Position in the projector menu that can move the image up about 10%.

Do these two methods operate identically other than the range? The manual states that the best image is when the Lens Shift is centered. Is that true also for Vertical Position? Is Vertical Position like Kestone Corrections in that it should be avoided?

Would the answers be the same for Horizontal Lens Shift and Horizontal Position?

Wild guess? Do you have a 1280x768 projector? If so, the first is optical lens shift, which moves the projected image up/down on the screen. The second is electronic shift, which moves the 1280x720 active image area up/down inside the 1280x768 native panel.

If this is the case, then there's no degradation using the vertical positioning, it's just moving unused lines to the top or bottom of the image. No, it's not like keystoning, and I'm unaware of anything similar in the horizontal direction.

While I am no means an expert and others feel free to prove me wrong.
The way it was explained to me is that adjusting the position in the menu is to be avoided because it changes the way the panels (LCD) have the image on them
While manual lens shift changes the position of the entire projected image

Sorry I did not mention the projector. It is a Panasonic AE2000U which has a 1920x1080 panel. Kind of mystery how a 1920x1080 image can be shifted around even 10% in the panel unless there are unused pixels.