What is the difference between Greedy-Search and Uniform-Cost-Search?

Nope. Your understanding isn't quite right.

The next node to be visited in case of uniform-cost-search would be D, as that has the lowest total cost from the root (7, as opposed to 40+5=45).

Greedy Search doesn't go back up the tree - it picks the lowest value and commits to that. Uniform-Cost will pick the lowest total cost from the entire tree.

In a uniform cost search you always consider all unvisited nodes you have seen so far, not just those that are connected to the node you looked at. So in your example, after choosing C, you would find that visiting G has a total cost of 40 + 5 = 45 which is higher than the cost of starting again from the root and visiting D, which has cost 7. So you would visit D next.

The difference between them is that the Greedy picks the node with the lowest heuristic value while the UCS picks the node with the lowest action cost. Consider the following graph:

If you run both algorithms, you'll get:

• UCS

Picks: S (cost 0), B (cost 1), A (cost 2), D (cost 3), C (cost 5), G (cost 7)

Answer: S->A->D->G

• Greedy:

*supposing it chooses the A instead of B; A and B have the same heuristic value

Picks: S , A (h = 3), C (h = 1), G (h = 0)

Answer: S->A->C->G

So, it's important to differentiate the action cost to get to the node from the heuristic value, which is a piece of information that is added to the node, based on the understanding of the problem definition.