"global" and "element" describe the way the problem is solved.
In the global iterative solver, the full g-size (i.e. global) stiffness matrix is assembled. The solver works on this single large stiffness matrix.
In the element iterative solver, a full system matrix is not assembled. The solver works on the collection of elemental stiffness matrices.
So, another stupid question about this then - when you someone might want to ONLY use the global iterative solver vs. the global and element iterative solver?
I am assuming that this option has been made available because there are cases where someone might ONLY want to solve the full g-size, assembled stiffness matrix vs. solving only the elemental stiffness matrices.
(This is fascinating stuff.)