When you are making changes to a specific object or rule, that object/rule is locked and you can see which admin locked it.
That means no other admin can make a change to that object/rule until the change is published or discarded.
The publish/discard action commits the changes to the management database and only applies to changes made in your session.
You can "take over" a session created by another admin if that session has not published/discarded yet as well.
When you install policy to a specific gateway, all published changes are pushed, whether that specific admin made those change or not.
As a general note, this question might be better in a more public space.
Mind if I move it?