This is a selection. It involves what used to be referred to as a "marching ants" or a moving dotted line. A selection can be made with a variety of selection tools.
[ATTACH=full]121411[/ATTACH]
A selection can be free standing or it can be made around a portion of an image.
Free standing...in other words not around anything in particular.
[ATTACH=full]121415[/ATTACH]
Specific selection around a portion of an image.
[ATTACH=full]121412[/ATTACH]
A selection becomes part of a "mask" only when it is used to create a "layer mask".
Once a selection is made into a layer mask, it's usually referred to as a "layer mask" or "masked area".
[ATTACH=full]121414[/ATTACH]
[ATTACH=full]121413[/ATTACH]
One needs to understand this when referring to selections and layer masks. One use for selections is to create layer masks. This however is not the constant rule. You can have an empty hide all or reveal all layer mask on a layer. It helps others to understand your questions if you are asking about selections or you are asking about layer masks.
Once a selection has been made and converted to a layer mask, the "selection" can be re-acquired by placing you cursor over the layer mask, hold Cmd/Cntrl and click.
Layer masks can be moved from layer to layer and form one document to another.
Other than what Jeff describes in post #4, another way to move layer masks (and subsequent selections) from one document to another is as follows:
With the selection active create a mask on a blank layer, select and copy (Cmd/Cntrl + C) the blank layer with the mask, paste (Cmd/Cntrl + V) the copied blank layer in the new doc, Cmd/Cntrl + click on the mask to make the selection active in the new document. Then you can save the selection in the new document.
The best way to move selections from one document to another is to copy and paste "paths". Then convert the path to a selection.
