A staff member will see all the details of their ticket, tickets that they created or if they have permission they can also view tickets belonging to other staff users or customers. They will never be allowed to reply to any ticket that they didn't create. This is an example of a Ticket that a staff member has created and as you can see there is the option to reply.
Depending on the role and permissions they have a staff member may be able to view other staff members tickets. They might be able to see their companies tickets or in fact all inbox tickets however they won't be able to reply to any of them. Only an Agent can respond to tickets not belonging to/created by them. See the example below of a Ticket within the system that this Staff member has permission to view however they won't be able to reply.