User own - each computer has one or more user accounts that are not admin/root, when you get access to the user of the computer, it counts as owning that user.
Root is when you get access to the root account of the computer - the account that has permissions to do anything it wants. Full control over the system.
To own a user you need to submit a user flag, which is located on the desktop of the user.
Each machine has 1 user flag but can have multiple users.
Root flag is basically a user flag for root/administrator account. There is always 1 root flag.