In the first example, the events are independent - rolling a 20 on one die doesn't make rolling a 20 on another die impossible, rolling a not-20 on one die doesn't make rolling a 20 on another die more likely.

In the second example the events aren't independent. One of the 20 must be correct, 19 of the 20 must be wrong, and so if you get one and it's correct the next must be wrong, and if you get one and it's wrong the next is more likely to be correct. The standard example here is actually playing cards (or pulling colored marbles out of a bag), where if you draw/pull one and put it aside it's no longer there for the next pull, and so the odds are different.