Being unhappy at work can be one of the motivation. For certain there are many others (wish to learn something else, wish to become the next big entrepreneur, wish to go solo). Many people can't just leave what they have, and they have a skillset that may get them to create a business, but not the required resources / contacts. A side project may be one of the way to start.

Agree on your second point - it should be called a side project. It's a startup / business from the day it actually _does become_ a business.