The reports you see under My Reports and Other Reports are either reports you or your collegues created or specific views of the canned reports that can be found as Venkat indicated.
In SP14, you should also have Web Reports in the Web Console, which have some overlap with the Java Console reports. In SP14 or 15 there are also reports in the Admin Console/Command Center which are similar to the Web Console ones or tied together somehow (I'm a bit fuzzy on that relationship).
Web Reports can also be scheduled and you can see the schedules from the Java Console but you won't be able to modify them there. You will need to use the Schedules section in the Web Console.
You can find more Web Reports in the online Store that can be installed into your CommServ and run. Most of them are Free.
I agree. Having one place to view reports would be nice. Right now there are about 4 places.