My understanding is that PDAF uses distances and movement as well as a way to help with tracking motion, it uses complicated software to 'predict' where the next shot should be. It's not simply a case of bringing two images together (although this is part of the process). I thought that Sony finished off with contrast detect too but my recent reading suggests that it's purely PDAF on the latest bodies which is what allows it to be as fast as DSLR, contrast detect still can't track as fast as PDAF. In AF-S it may well still be finished off with contrast detect, I don't know.
In AFS it uses contrast detect to finalise, thats why its much slower in afs.
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