Without implementing osTicket (at least in a demo environment) its a little hard to explain some of these things.
Users can be added to Organizations.
Tickets opened by users in the same Organization can be automatically shared between the users (by using Collaborators).
Collaborators are (users) who have also been added to the same ticket. They can interact with and reply to the ticket. But only the user that the ticket was opened for actually owns the ticket.