Trusted means that an authenticated account from one domain isn t rejected by another domain. Contiguous DNS domains means that they all have the same root DNS name. Stanford.edu are not contiguous. A tree shares common global catalog servers, and a common schema. The schema determines what types of objects, classes, and attributes may be created of all the domain databases in the tree.
Trees have no physical representation like a domain controller.
Trees are used to group Windows domains which have a reason to share files, policy, and resources. A Windows forest is a group of 1 or more trusted windows trees. The trees do not need to have contiguous DNS names. A forest does share a schema and global catalog servers. The Windows domain win.