The Bachmann knot is used to support a load on a vertical rope. It slides down the climbing rope freely, but solidly grips the rope when loaded. To release the knot you just need to unclip the top loop and pull the line free. It is safer to use the knot with the carabiner gate opening facing down.
The Prusik grips tightly when loaded, but without a load slides freely up and down the rope. It can be tied with one hand and does not damage the cord. However, the Prusik tends to jam. It is principally used for attaching loads to a cord or for making the cord easier for climbing.