BST cannot have same shape for particular set of data

Suppose you have to insert three elements

Input sequence matters in a BST

Suppose you have input sequence

1,2,3

BST will be

1

2

3

But if your input sequence is 3,2,1

Then your tree will be like

3

2

1

For particular set {1,2,3} you can have many BST possible and shape changes.

Now answering your doubt

A BST with a set of elements always have multiple links per node.

This statement is correct because A BST is a Structure where each node has more than 1 links, one pointing to the left sub tree and one pointing to the right sub tree

always have multiple links per node – Confusing but true

Actually there is always two OUTGOING pointers even in leaf nodes, the only difference is that in leaf nodes these two left , right outgoing pointers are null