The fast first pass compares a question to a chunk with no view of either. A second pass reads both together and scores the pair, which is slower and much better. Two stages, cheap then careful, is the standard shape of a good retrieval system.
About 1 min of reading
Before this new lesson, one small question about the lesson you just finished. Recall it, do not look it up.
Widen then narrow.
Wide first
Before you run it, say out loud what it will print. Then open the answer.
Careful second
Before you run it, say out loud what it will print. Then open the answer.
Read the first example one line at a time. A line that prints shows what appears on screen; the rest set things up quietly.
The first stage should pass more than you need, since the second stage is what picks. A first stage at k=3 and a second at 3 can only reorder three, which is a second stage that does nothing.
A candidate strong in both stages is the best evidence. Keeping both scores makes the final list explainable, which is what lets a reviewer see why an answer cited what it cited.
The first stage takes the top few dozen cheaply. The second reads the question against each of those and reorders to the best few. The answer only ever sees the final few.
A question asking for what is not supported and a chunk describing support point the same way to a vector model. Reading both together, the second stage sees the mismatch that the first could not.
The second stage costs per candidate. Passing a hundred candidates is a hundred reads per question, so the first stage has to be good enough to make the list short without cutting the right chunk.
Each one is defined here on this site. Open the entry for the full definition and the other words it points at.