What's the difference between a cheater stick and a stick clip? Do I need both?
Both items are sticks that you rig a quickdraw to, and use to reach up and clip a piece of gear, usually a bolt, that is out of reach. Now, the actual name of the device will vary depending on how it is used. Imagine that your name is Richard, but some people call you Dick. You get the idea.
When you take a stick up on a big wall and use it to reach past a cruxy placement, saving you time or sparing you from certain death, or perhaps both, you are cheating. Therefore, you are using a cheater stick.
Now, while sport climbers think that all aid climbing is cheating, when they use a stick to clip the first (or even second) bolt on their route, potentially saving themselves from a nasty ankle wrenching, it is not cheating. Never mind that said bolt is usually at a height regularly soloed by children, drunks and hillbillies hot after shiny snaplinks. To the sport climber, using a stick clip just seems like the smart thing to do.
Does the distinction seem arbitrary? Find happiness in nihilism, the belief that everything is arbitrary, and whatever choice you make will be as empty and meaningless as the option.