To make up is to invent a story — or to become friends again after a fight. Two senses with nothing in common.
The inventing sense is used about excuses and tales, so making up a reason means producing one on the spot. The reconciling sense takes with, and making up after an argument is what everybody hopes will happen. There are two more: making up a number means completing it, and making up time means recovering a delay. The noun makeup covers cosmetics and, quite separately, the composition of something.
Middle English
maken up
English, today
make up
From Middle English maken up, equivalent to make + up.
Etymology from Wiktionary, CC BY-SA