The way the cases are set up, it’s not clear to me that B advances any argument at all. In the first scenario, A makes a twofold claim:
(1.1) Event XY happened.
(1.2) All XY-type events are miracles.
The conclusion is that a miracle happened. Now, B responds by rejecting (1.2) – and a rejection of a premise/claim isn’t in itself an argument. Of course, B may support her move by providing a natural explanation for XY; but providing an explanation also isn’t in itself an argument.
If there is an argument here, it would be a meta-theoretic argument, to the effect that natural explanations are in some sense better than explanations that reference miracle. What the meta-theoretic argument is exactly, would depend on the details of the case. It may be an instance of Ockham’s Razor; but it may also have to do with the fact that natural explanations have more predictive power, are simpler, can be tested, …
In the second scenario, A makes the same twofold claim as before (except we’re talking of WZ and not XY). Yet this time, B responds by rejecting the first part of the claim, rather than the second. Once again, a rejection isn’t in itself an argument. As before, B may support her move – say by pointing out that the historical sources that speak of WZ are unreliable.
This could again be interpreted as a meta-theoretic argument: assuming that the sources are unreliable, is theoretically better (whatever that means exactly) than accepting that a miracle occurred.
Now, there is a slightly simpler (and much less detailed) way to look at the situation. It seems that B firmly accepts the following claim:
(3) There are no miracles.
In turn, if you combine (3) with (1.2), it logically follows that (1.1) is false. Likewise, if you combine (3) with (1.1), it logically follows that (1.2) is false. The first implication is an instance of modus tollens, the second could just about count as a reductio ad absurdum.