Use BreadthFirstScan & DepthFirstScan on graphs?

Questions
1

Greetings,
I play with the functions of the subject matter.
And I’m having a hard time understanding the difference

  1. Events that provide access to vertex visits
  2. Events that provide access to vertex discovery

I would be very grateful if anyone would enlighten me.
Thanks, Dani

2

Thank you for your detailed answer:
https://mathematica.stackexchange.com/a/214114/69556