The $12-a-jar difference.
What’s the difference between an $8 burger and an $18 version? Calling the swipe of mayo on the bun aioli. Kidding aside, American eating has essentially defined aioli as fancy flavored mayo, usually flavored with garlic but also blended with everything from black truffles to chipotle chiles.
In France and Spain, though, aioli is a different sauce entirely. The word derives from the Catalan words for garlic and oil, and in a traditional Catalan allioli, that’s all there is to it: raw garlic cloves whipped with olive oil and salt into a fluffy, creamy condiment. Some versions of the sauce are emulsified with egg yolks; others with moistened stale bread. But few fit the definition of mayonnaise, an emulsion of egg yolks, oil, and often acid, no garlic required. True aioli is breathtakingly pungent, not the mild creamy stuff we smear on sandwich bread.
Try making your own by combining minced garlic and olive oil in a mortar or with an immersion blender. Just don’t expect to kiss anyone afterward.