When I saw the original Star Wars saga as a kid, the concept of the Dark Side imprinted in me was quite simple. You did a bad thing, so you're a bad person so you go to the Dark Side and keep doing bad things.
Now, obviously this doesn't hold true in reality. In my mind it is perfectly reasonable for Luke to kill the Emperor and Vader and then just flee the Death Star and rejoin the Alliance. After all they are at war, those are enemy officers that have captured him and are taunting him by threatening with death of all loved ones and the whole operation was intended to kill the Emperor anyway.
The same would hold true for Anakin. He could have killed Mace Windu to save the Chancellor and Padme but that doesn't mean he's going to then go mad and kill all Jedis including children. It doesn't add up from a merely psychological point of view. He had a set of objectives and that made him want to keep the Chancellor alive (quite valid by the way, Mace Windu is quite clumsy on that) but just after killing him he goes into "Yes master I'll do whatever you say" which from a normal point of view will NEVER ever make sense.
In both cases it seems like the assumption is once you use the Dark Side you completely turn to the Dark Side and become a different person that you were before. That would be coherent with Anakin "dying" and Vader being born.
Is that the way the Dark Side works? Is there any canon information about what happens when someone turns to the Dark Side? Specifically to whether they become a different person or how he or she actually changes?
Note: Vader is angry after he finds out Padme is dead, even though he's already turned.
Example of what I mean. In Buffy they explain how people that turn into Vampires lose their soul and it's taken over by a demon, and thus they are, in all effects, a different person with their memories.