Nope, they are totally different. However, the DB gem is an interface/driver similar to PHP's PDO, while AR is a set of drivers, interfaces and high level ORM interfaces. In theory, one could probably use DB as a driver under AR. One person even basically uses AR to generate SQL and then executes it with the DB gem, which I thought was pretty clever.
Yes, it was. It was originally a front end and back end (query server) for CouchDB. But CouchDB 2 really went in a different direction to what I expected with query servers so I gave up and decided to pivot in a different direction with the code base.