Ken Mandelbaum answered this pretty well in his 10/15 column on Broadway.com:
Q: I've never been able to figure out the difference between an understudy and a standby. Can you help me out? How about a swing?---David Little
A: In general, an understudy is in the show's cast and moves up to substitute for an absent principal. For example, Brad Oscar played Franz Liebkind in The Producers while understudying Nathan Lane's Max Bialystock. When Oscar went on for Lane, Oscar's understudy played Franz. A standby is usually a performer who is not in the cast, but is hired solely to cover a principal. In the current Gypsy, Maureen Moore is Bernadette Peters' standby; she plays Rose in the event of Peters' absence but does not otherwise appear in the show. (Moore was similarly a standby for the roles of Norma Desmond in Sunset Boulevard and Fraulein Schneider in Cabaret.) Swings go on in place of ensemble performers, and are usually trained to cover more than one such player in a production.
There are plenty of shows, though, where the understudies are not regularly a part of the ensemble.
"Gif me the cobra jool!"