Difference between cross edges and forward edges in a DFT
Wikipedia has the answer:



All types of edges appear in this picture. Trace out DFS on this graph (the nodes are explored in numerical order), and see where your intuition fails.


This will explain the diagram:-

Forward edge: (u, v), where v is a descendant of u, but 
not a tree edge.It is a non-tree edge that connects a vertex to a descendent in a DFS-tree.

Cross edge: any other edge. Can go between vertices in 
same depth-first tree or in different depth-first trees. (layman) It is any other edge in graph G. It connects vertices in two different DFS-tree or two vertices in the same DFS-tree neither of which is the ancestor of the other.(formal)