Why does my JavaScript code receive a No Access-Control-Allow-Origin header is present on the requested resource error while Postman does not

Question

This question is about why XMLHttpRequest/fetch/etc. on the browser are subject to the Same Access Policy restrictions (you get errors mentioning CORB or CORS) while Postman is not. This question is not about how to fix a "No 'Access-Control-Allow-Origin'..." error. It's about why they happen.