Maybe I'm wrong, but I think they are the same thing.  One company might call them a Bringdown and one might call it an Update.  I DO see Bringdown used more frequently when it is the update that is conducted just prior to recording the document.  Usually if we are doing an update prior to closing because the process took to long to close, they call it "update".  I wanted to add that I charge more if I am updating someone else's work and I disclaim that on my report, since I have no idea if that person was reliable or not.