This [Wolfram](http://mathworld.wolfram.com/CompleteBinaryTree.html) link talked a bit about 'Labelled' Binary tree. So is there something called 'Unlabelled' binary tree as well ? A concise explanation of Both would be really nice.

Why am i searching for this ?  

I'm trying to answer this question :   

> 
> We are given a set of n distinct elements and an unlabeled binary tree with n nodes. In how many ways can we populate the tree with the given set so that it becomes a binary search tree?
> 
> 
> 

Now, i know the number of Binary trees given n nodes is the nth [Catalan number](http://en.wikipedia.org/wiki/Catalan_number), but now i'm confused : which of the above two types does this formula apply to then ?

PS: some help with the question in quotes would be very nice too :)