This is a simple question from algorithms theory.
The difference between them is that in one case you count number of nodes and in other number of edges on the shortest
Simple Answer:
Depth:
1. Tree: Number of edges/arc from the root node to the leaf node of the tree is called as the Depth of the Tree.
2. Node: Number of edges/arc from the root node to that node is called as the Depth of that node.