(A) describes an argument where the author is citing new evidence that questions the validity of an argument they disagree with. An example of this could be "you claim that the appearance of flat land proves that earth is flat, but the curvature of the earth is clearly visible on the ocean."
(B) Describes an argument where the author uses the same evidence as the argument they disagree with, but proposes that the evidence proves something else. An example of this would be: "You claim that the existence of dinosaurs proves that lizards are smarter than humans, but this is not true. Their existence proves the opposite, as they failed to defend themselves against the meteor.
While both of these are ridiculous arguments, hopefully they help to illustrate the techniques.