Space/Time complexity:
BST
Space : O(n)
Time:
Insert: Best - O(log n) and Worst - O(n)
Delete: Best - O(log n) and Worst - O(n)
Search: Best - O(log n) and Worst - O(n)
Self balancing BST
Space : O(n)
Time:
Insert: Best - O(log n) and Worst - O(log n)
Delete: Best - O(log n) and Worst - O(log n)
Search: Best - O(log n) and Worst - O(log n)
As Red Black tree balance its height, that's why manage Insert/Delete/Search operation in O(log n) in the worst case as well.