BSON actually was considered as the JSON storage format for PostgreSQL, but was discarded once people figured out that BSON stores ["a", "b", "c"] as {0: "a", 1: "b", 2: "c"} which is just silly.
wow.. thanks for that info, i came here to see the diference and and a little shocked by the silliness of BSON (and the team that created it, apparently Mongo); compared quality devotion of the postgres community..
jsonb is the name of a data type used in postgres in order to store, index and update JSON. bson is the same used by MongoDB and also made a semi-official standard.