Q: Can a binary search tree be skewed? What I am trying to ask is whether a binary search tree is self-blancing or if it can also become skewed?
I tried looking for an unbalanced binary search tree and could not really find anything.
So is a BST different from a self-balancing BST?

A: 
is a BST different from a self-balancing BST?

Self-balancing binary search trees are binary search trees which have logic added to them for keeping the tree more or less balanced.
So every self-balancing BST is a BST, but not every BST is self-balancing.
In fact, with a binary search tree we can refer to a data structure without any algorithm that goes with it. For instance:
               4
              / \
             2   8
              \
               3

This represents a binary search tree. Nothing more needs to be said about how you would insert or delete a node. It might even be immutable, not allowing any insertions or deletions. It still is a binary search tree.

Can a binary search tree be skewed?

Yes. The following is a valid binary search tree, although not one that will allow for efficient look-ups:
                     5
                    /
                   4
                  /
                 3
                /
               2
              /
             1

A self-balancing binary search tree, is one that has specific algorithms associated with it for insertion and deletion that will include rebalancing logic.
There are many different self-balancing binary search trees:

*

*AVL tree


*Red-black tree
Variants:

*

*AA tree



*B-tree
Variants:

*

*B+ tree



*Splay tree


*Treap


*Scapegoat tree


*Tango tree
