All deceased people entered into FamilySearch FamilyTree are entered into a SINGLE collaborative database (of billions of records) that we all share. (this is a paradigm shift from Ancestry where each person has their own disjoint database).
I suggest watching this great video.
You cannot, and you cannot have your own tree. There is only one tree in FSFT and it is owned by FS. All of us are allowed to add to and improve that one single tree.
As others have said there is only one tree but you can have more than one account or access to more than one account. That may be more what you are really interested in. When you log in you see recently added info about some of you ancestors, people you have recently viewed, other info related to your account. If you are searching for a friend then some of their stuff will be mixed in with yours. If you have more that one account you can keep all of that separate. I am far from an expect with FamilySearch Tree and only recently discovered this forum. I don't know if FamilySearch evens approves of multiple accounts but I figured out long ago that I needed more than one. Each one has a separate log in and email address. One thing you might do is have your friend set up an account (or with their permission you set up one for them) and they give you the log in info. There is something called a helper number that allows others to edit your "Tree information" but I am not totally sure what that allows that anyone can't already do. Good luck!
Yes multiple accounts is one option - but in most cases there is no need for it.
You can easily keep track of two or many different famil tree groups (that are all subsets and part of the single one database we all share)
Creating a browser bookmark for each different family group (and using with a single FS account) would be one very easy option to quickly navigate from one family to another - when the families are not really related in any close way.
Really there are few things you cant handle with one account.
Bumping into the limits of the capacity of Family Search memories for a single account - is one of the few reasons I have seen a real need for multiple accounts (but that after going higher than 15,000 items - which most people will never get to)
"If you have more that one account you can keep all of that separate"
Actually that is not true. Only account specific data can be kept separate. That includes things like activities list, To-Do list, messages and LIVING individual records, etc. The full enormity of the single FamilySearch FamilyTree with all of the records of DECEASED persons in it (1.3 billion records) appears exactly the same to all FS patron accounts.
The FSFT is for recording family history and records as they are found and documented. It is not suitable at all for setting up temporary or experimental family trees in order to do "what if" type reasoning. Anything that you change in the tree will be seen by all other FS account holders and flagged to anyone who is following the records that you have modified (they will come looking to find out why the records that they have worked on has been changed by someone).
The hints engine's logic is based on the current contents of the FSFT database. If you start putting experimental or theoretical trees in place, it will affect all hints surrounding those individual's records. Furthermore, if you have created duplicates of records already in the tree, hints may not be given to you.
In these and many other ways, familysearch.org is totally different in both function and intent than ancestry.com.