Dichotomy: A pair of categories that are mutually exclusive, and exhaustive.
A dichotomy can be a powerful tool, as it quickly categorizes things by essentials, and you can understand a lot based on them. Some common dichotomies in life include True or False, Right or Wrong, Fact or Fiction, Asleep or Awake, and Cost or Benefit. There are countless numbers of them. They don't always have unique words for each half. They can include "listening or not listening", "driving or not driving", "color or black and white", etc.
Since dichotomies are so useful, a false-dichotomy can be quite harmful. A false dichotomy can occur when a pair of categories are not really mutually exclusive, or are not exhaustive. For instance, the view that you have to sacrifice yourself to others or sacrifice others to yourself is a false dichotomy because it ignores the possibility that your actions can benefit you without hurting others. Or saying a governmental policy must be for the rich or for the poor is a false dichotomy because it can benefit both.