In All unsolved you find all Tickets with the status new or reply. 

In All open you find all Tickets with the status new, reply, pending or solved.

If you want to find an old Ticket with the status closed, you need to go to the search field in Tickets, select closed below Filters and click SEARCH. See below.

If you know which Ticket you're looking for, you can also type it in Search... at the very top.

You can also create your own filter in My Views to gather all Tickets with this specific status. Take a look at the article Why do I want and how do I create My Views in Tickets? for more information.