Ok, with the text of the Fourth Age stuff in front of me I can explain the context.
First, they are both excerpts from histories. Notice that everything in both of them is in past tense.
Second, the first one is about the Breaking of the World and mentions "him they named Dragon". Note that 'Dragon' is an original name they gave him, not a previously existing identifier. It may have had a previous meaning, but it was not associated with one particular man before.
Third, the second one goes on in flowery language about the return of the Dragon - "Let the Dragon ride again on the winds of time." The event it talks about is therefore after the Breaking of the World - and I'm sure you've figured out by now that the true Dragon has not returned at any point between the Breaking and the start of the series. Thus, it must be a history written after the events in the series, and I don't think it's much of a spoiler to say that we're working towards an Age transition.
The prologue occurs at the very end of the Second Age, also known as the Age of Legends. The series proper occurs near the end of the Third Age. The two excerpts at the end of the prologue are from histories written early in the Fourth Age after the end of the series.