First of all, there is a lot of misunderstanding about the Graph search and Tree search. The difference between these two is not about Graph and Tree. They have two different algorithms. You can find the difference in the first answer in this link: What is the difference between graph-search and tree search?.
So now I want to be sure that I have understood these two searches well. We have a graph search and a tree search for each searching algorithm. For example BFS graph search and BFS tree search. Or DFS graph search and DFS Tree search (DFS tree search is not complete for example). Iterative deepening graph search and Iterative deepening tree search.
Please answer if you are well informed in this subject because as you see in the above link many users have answered the question wrong (the difference between graph search and Tree search)