What information persists after system restoration?
I'm a guy who is pretty experienced dealing with Windows but quite a novice on the Mac.
A current project is to help someone who fears having had malicious software secretly installed on a couple of their Macintosh computers. The one I'm experimenting with is a MacBook Air. My first attempt at system restoration involved booting into the recovery system and using it to erase, which I think means reformat, the partition used to run OSX. Subsequently the system was restored to this partition, which seemed to involve the Recovery System downloading from the Apple Store what ever files are needed and rebuilding the system.
The result appears to be a pretty clean system but to my surprise there seems to be some information present that could only have come from the former system, which I'm trying to replace. Insofar as I was expecting the operation to completely restore the system to the same state it would have been if newly purchased this result causes me to ponder what else may not have been restored. My objective is to be confident that the system has no extraneous software installed when I get done with this operation, which is something I cannot say with confidence now.
A plausible explanation is that I don't understand how certain devices on the Mac work and that the persistent information pertains to the preservation of state within attached devices. In this case what I've recognized is that there are bluetooth devices, formerly used on the computer, that the system (e.g., OSX) seems to be trying to find. Why is that? If my surmise is correct, how is one supposed to learn about the behavior of such devices? In that, what else has been left on the computer? How can I completely restore the computer to it's initial state?
MacBook Air, OS X Mavericks (10.9)