Diagram

Two ways to look up "server unreachable"

Left: an inverted index maps each word to the lines that contain it. Right: a vector space places lines as points, and the query lands near lines with a similar meaning. BM25: a word list server d2, d3 unreachable (no line) port d1, d5 memory d4 Hits only lines with a shared word. Vectors: a map of meaning query d2 d1 d5 d4 d6 Hits the nearest lines, words or not.
BM25 looks words up in an inverted index, so "unreachable" finds nothing and only "server" scores. A vector search embeds the query and returns the nearest lines, so it can find the connection error that uses none of the query words. The map is a sketch, not a real projection.