In control flow graphs, what is the difference between a path and a branch?
I do not know the exact definitions used by your class, so I am saying this with caution. A branch normally correspnds to a graph edge that allows control to pass from one node to another in the graph. A path is a succession of edges connected to each other, with possible repetition and representing the successive parts traversed by the control. So a branch will be a element of the program structure, a static entity. The path represent a fragment of computation.

If you say more about what you understood, I may be able to tell you whether it makes sense.