See Jean-Louis Cazaux's excellent page on this topic,
http://history.chess.free.fr/enigma.htm
Shatranj and Chaturanga would seem to be the same game, although,
generally speaking, one thinks of Shatranj as the Persian game and of
Chaturanga as the Indian game. The two can't be differenciated, it seems.
There are also possible influences from China.
As far as 'recognized' goes, I would tend to think that both
'Chaturanga' and 'Shatranj' should be recognized, if for no other
reason that the CVP articles on these games suggest that the Indian game
migrated to Persia. Not 'recognizing' Chaturanga would seem to ignore
this root.
Perhaps the uncertainty in the history should be reflected in the
'Recognized' variants list.