Both are the same thing. The sandbar is where the stingrays gather and yes, it varies from a couple of feet to neck deep. Of course you can go into deeper water, but there is plenty of area where you can easily stand.
The Stingray City may just be the name that particular tour company gives that tour but they all go to the same place.
Carnival Cruise Lines:
Fantasy 90, Celebration 95, Victory 05, Conquest 05, Spirit 6/06, Freedom 6/08, Holiday 7/08, Victory 6/09, Valor 9/09, Dream 6/10, Splendor 8/10,Conquest 8/11,Magic 11/11,Triumph 4/12,Spirit 7/12,Freedom 11/12, Triumph 2/13 - The fire cruise, Magic 1/14
NCL Dream October 2006, RCCL Mariner OTS June 2007, Celebrity Silhouette 2013