Rearrange/rename GlobalScreenshot methods

Moves methods to a more logical order (public/protected methods
before private, make method order closer to logical flow) and
renames the various takeScreenshot methods to better distinguish
them from one another.

Bug: 160325487
Test: manual (rearrangement/renaming only, no logical changes)
Change-Id: I113608b9638383e615404dbfd89e032327f9e3ca