Mayonnaise is a simple sauce, made by combining egg yolks and oil. It is used widely — from salad dressings, to spreads, to dips. It’s very quick, easy, and safe to make — and the homemade version is a far, far better sauce to make than you can ever buy. There’s really no excuse for bottled mayo. Aioli is just a spiffed-up version of mayonnaise, with garlic, lemon, and sometimes herbs. You can play around with almost any combination of oils, and seasonings, and make spectacularly good aioli, in about 5 minutes.
When Maggie lived at the Normandie house, she made aioli regularly (we ended up calling it Maggie sauce). At some point, we had to tell her she was forbidden to make it again, because we were eating it by the spoonful, right out of the bowl.