Booker and Comstock are the same person from different realities. In the baptism scene, Booker's choice (to be baptised or not) essentially created two alternate realities, one where he accepted it and became Comstock, and another where he rejected it. Elizabeth is Anna, she was taken by Comstock because he realised he was infertile, so he used the Lutece's machine to look into other dimensions to find a child of his own.