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Booker and Comstock are the same person.

Both Letuces are actually the same person.

Anna and Elizabeth is the same person.

In one timeline, Booker was guilty for all the wrongs he did and got baptised. At that point, at least one version of Booker (looking at parallel timelines here) became Comstock.
In Comstock's timeline.. Letuce (the female one) developed a time machine by mistake. Comstock used this and became quite powerful. It is in using the time machine, where Anna, second Letuce (male) and Booker finally come into play.

The time machine usually jumped into other universes, hence changes done in that timeline never affected comstock's timline. From using the time machine a lot, Comstock became impotent and in wanting a child to be his heir, he crafted this plan to steal one of his progeny from himself in another timeline.
Letuce contacted herself and planned this out. In some timelines, she was actually a guy.

The whole backstory is quite good. Read the link here. It gives a lot more information than i could even begin to type.

http://bioshock.wikia.com/wiki/Rosalind_Lutece