check out these videos - to better understand the collaborative nature of the ONE SINGLE family tree - that we all share.
WHY USE FAMILYSEARCH FAMILYTREE
You can you this screen to locate anyone in the common family tree database
There are no other editable family trees in the FamilySearch FamilyTree other than the single shared FamilySearch FamilyTree itself. the FSFT site is totally different from other sites like Ancestry.com where everyone gets to create and control their own "personal" trees. The FamilySearch FamilyTree is a single tree that anyone can modify and improve.
That being said, FS does have a database separate from the FSFT that contains Read-Only trees that have been submitted by other people from their own collections and collected by the church. This is the "Genealogies" database. For example, when a person uploads a GEDCOM file, it is put there. Even the owner that uploaded it cannot modify it once it is in the Genealogies DB (although they can later remove it if they want). The database also contains other tree related records that have been submitted over the years from other legacy sources such as the International Genealogical Index (IGI) and the Pedigree Resource File.
This database is searchable by going in through the "Search-Genealogies" menu function. Note that most of those records have no real sources identified, although GEDCOM files that have been uploaded may contain notes that ARE visible when examining the results of searches.