Good lord. Do I have to explain everything??  It’s not “carrot or stick”. It’s “carrot AND stick”. The phrase “carrot and stick” is not meant to imply a choice between pain and pleasure. It is meant to suggest motivation by the placement of  a reward that is always just beyond reach. It’s motivation for donkeys, oxen, and the physics challenged. And the talking heads who read news in front of cameras.

This is what is meant by "carrot and stick"