To what exactly does the "carrot-and-stick" metaphor refer?

For most of my life, when I heard the reference to the carrot/stick, I would visualize a beast of burden (horse, mule, ox, etc.) who does not wish to pull the load (cart, wagon, etc), being enticed by the promise of a carrot as a reward, as cited in this article. It seems that over the last couple decades (subjectively speaking), there has been a drift of meaning of the metaphor, referring to the carrot as the reward and the stick as punishment, as per the Wikipedia article. Which of these is more accurate?