A tree is not a linked list. A tree (be it binary, or n-ary..) can be implemented using linked nodes, similar to a linked-list; or using an array and indices to reference the children and parent (i/2=parent, 2i=left_child, 2i+1=right_child, I think..), and there are other ways still.
The term Tree refers to the idea of a tree structure, independent of implementation. The term Linked-List (they can be singly or doubly-linked) refers specifically to the notion of nodes being linked to one another to give a linear list of nodes.
If a binary tree is implemented as linked nodes, then it is somewhat similar to the implementation of a doubly-linked list. A linked-list in this case is almost identical to a binary tree where each node only has left children. However, once that tree acquires a right child, it is no longer a linked list (as long as the right child is not the node's parent! But then, it wouldn't be a tree any longer, but a graph with cycles..).
Sorry to elaborate, but that was a nice refresher in my mind as well!