Session sharing is often a confusing point for our users and I find I get plenty of questions in regards to it. Thus, I decided that someone, certainly, would benefit from an overview.
1. When you share a session, it puts a copy of that session on the selected user(s) lab/demo page.
2. Only an SE Admin can act upon the original session (schedule it) - other users just get to poke around. Another SE Admin can even cancel/change the owner's schedule of that demo/lab.
3. If it's a "full" or "resources only" share, and the owner schedules it, other users will be able to access the VM when it is available. If it is just a "copy only" share, a user will get as far as the launch pad for the session, but not actually be able to access the VM. It looks a bit misleading if you don't read carefully (like me).
4. The copy button (when in "full" or "copy only" share) exists on the overview page. A user can have his own app session by clicking this. He is then free to manipulate that instance as he would a lab/demo he created himself.
Hopefully this is helpful. If not, pretend, and leave me to my disillusions.
Jackie.