I'm always slightly amused by debates about whether to use a reward or a punishment to promote certain behavior. For example, should Massachusetts encourage universal health care by fining people who aren't covered (as they do now), or should they give people who are covered a tax break? Should Jimmy get a trip to Disney if he passes all his classes, or should we cancel the family vacation to Disney if he fails?
I think the second example demonstrates why I find the reward/punishment dichotomy amusing. It's often just semantics. If Jimmy gets passing grades, then he'll end up in Disney. If you don't have health insurance, then you'll shoulder more of the Massachusetts tax burden. Some punishments are clearly punishments (imprisonment), some rewards are clearly rewards (a trophy), but especially when dealing with large groups, you're redistributing some benefit/cost, not explicitly rewarding or punishing.
It seems to come up in taxes a lot. Taxing a segment of the population is unpopular, giving tax cuts to another group are fine. So rather then punish polluting firms, you reward non-polluting firms. Rather then tax increases for the poor, you cut the taxes for the rich and let inflation bring things back to a balance. Amazingly, wording something as a reward or a punishment can make all the difference.
Thus I propose a new term in the vein of "carrot and stick" already used to differentiate between rewards and punishments (as an aside, inaccurately. The term probably comes from tying a carrot to a stick to lead an animal, not beating it while feeding it to a tasty treat). "Carrot" is a reward, "Stick" is a punishment, and "Carrot Stick" is a case where it's both. You can feed a carrot stick to your donkey, or you can hit him with it (possibly ineffectually, but it's a metaphor). What a versatile tool those pre-cut veggies are!