If I'm reading the original question correctly, you want to move just the "Marching Ants," not what's inside them. I think I have the answer, verified by fiddling just now with CS-4: Once you draw your original selection, don't change any tools, just click inside your box or circle, hold and drag. This only works, though, if you've clicked on the far-left "New Selection" box up on the Tool Options Bar. This is the program's default choice, but it is "sticky," meaning that Photoshop will remember your setting, even after you start up the next day.
Alternatively, you can right-click (or Control-click on a Mac) inside the marching ants and choose "Transform Selection". Then you can grab corners, distort or move the whole selection around to your heart's content.
(As for those four odd little boxes, does anybody else get unpleasant flashbacks to "Venn Diagrams" from grade school math class?)
--Anyway, the "New" button is what you'd expect.
--"Add to..." means that you can make a second selection without automatically erasing your first one. It can touch the first one, but doesn't have to. (You can select two eyeballs, or make a snowman.)
--"Subtract from..." means that if you make a little second selection inside a big first one, you'll wind up with a doughnut, bagel, tire, you get the picture. Visualize a rectangular doughnut and you're still with me.
--"Intersect with..." means that your final selection will cover only the area that includes both of your previous choices.
"Shift" is the temporary shortcut for "Add to..." and "Alt" (Option) is the temporary shortcut for "Subtract from..." The nice thing about using them is that they aren't sticky, so you won't get frustrated the next day trying to figure out why your selections don't act right.
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