At British Airways Long Haulthe Purser is the person who is actually in charge of any particular cabin area. Thus there will be a Purser in charge of WT, CW (2 on 747 both areas up and downstairs), and F.
Without being too technical the CSD had could be called (as TWA did) the Inflight Service Director whose reponsibility is to ensure the service delivery over the whole aircraft. They have no serving duties and should really be resolving any problems as and when they occur. They decide who works in which position and will make any changes accordingly.
To the best of my knowledge and belief there is not an equivalent in any US carrier (again I am talking transatlantic) they have a Purser but the title means that they get to do all the paperwork and bar counts. They have no management authority over any of the Flight Attendants and can not give them any instructions. Thus they are paid for responsibility but have no authority. They have serving duties - usually in F.
On Short Haul, CSDs are a dying breed as you only ever got them on aircraft that were big enough to warrant them - the 757 and 767 (when this came off mid-fleet). Pursers were on 737s and A320s and anything smaller. Essentially the job was the same.
As with American carriers all the terminology comes from the sea faring days (Cabins, galleys etc etc).
Hope that helps
PG