If you have contents of an axes (lines, surfaces, drawn text) that you want to move while the axes itself stays in one location, then use panning to adjust what is visible in the axes (by either using the pan tool, or by adjusting the axes XLim and YLim)
When you have a collection of objects that are to be moved within a figure while the figure itself stays in one place, such as the position of axes, or position of controls relative to the figure edge, then put the collection inside a uipanel and have slides adjust the location of the uipanel relative to the figure.
The above is enough in most cases, but if you need a uipanel itself to move, then put the uipanel within a uipanel. And if you need that to move, put it within a uipanel. And so on. It's uipanels all the way down!