actually, it's the same Batgirl, different "universe". In the comics, yes, Barbara Gordon gets shot by the Joker in a sickening display of his insanity. Her legs are no paralized, so she operates as a computer hacker called Oracle. In the cartoon, it's still Barbara Gordon, but with a different fate. In Return of the Joker, after the Joker commited another sick display of his insanity to Tim Drake Robin, Batman swore never endanger another young partner. As far as we know, he simply took away Babs's Batgirl suit, and she eventually became the new Commisioner Gordon when her father retired.
Now, you there isn't much in the way of "other" Batgirls. Before Barbara Gordon came on the scene, the 50s saw the presence of the duo Batwoman and Bat-Girl. And the current Batgirl is this asian girl whose mask covers her ENTIRE face, and she doesn't even TALK, which is no fun at all for us ticklers.