I like people's House Rules, I really do, but it would be kind if you would qualify that you are talking about House Rules when you explain, just for the sake of the OP and the people who have gone into detail about how the RAW defines it.
RAW: Outsiders who are called (planar ally, gate, etc) or travel physically to the Material and slain die permanently (barring certain spells that bring them back), just like anyone else. Any summoned creature goes back where it came from after being slain, including all those Magical Beasts, Animals, and Outsiders with summon spells and the demon and devil's summoning abilities.
In my campaign, I make slain Outsiders' "soul" (which is their very being) eventually reemerge on their plane of origin. High ranking fiends might be permitted to keep their station and memories/abilities, although many have their personalities destroyed and are reformed, hopefully this time serving their masters better. This process takes 101 days, and the corpse stays behind for a while, though it rots more quickly than most corpses, leaving the area around where it died desecrated.