In her memories, Sister Joy was a nun who cared for injured birds as a sacred practice. The Founder eventually recruited her to the X-Men.
In reality, Rapture is a nanotech creation created to aid Cerebro in achieving its "dream", the capture, categorization and storage of all mutants.
Cerebro's X-Men succeeded in kidnapping Shadowcat and defeating the real X-Men but later failed to capture a mutant-tracking satillite due to interference from the real X-Men.
Rapture and the rest of Cerebro's X-Men were later absorbed into Cerebro and destroyed in order to grant Cerebro enough strength to defeat the real X-Men.
