Mayonnaise is an emulsion of egg yolk and a neutral oil (often with vinegar or lemon juice and seasonings). Traditional aioli is an emulsion of mashed garlic and olive oil (and salt)—the name literally means garlic and oil. Food Network notes that true aioli starts from garlic and olive oil, while mayonnaise uses egg yolk and neutral oil.
In practice the line is often blurred: many modern “aioli” recipes add egg yolk (or start with mayonnaise) and garlic flavoring. Restaurants frequently label garlic-flavored mayonnaise as aioli. Shortcut versions can taste great, but they are not classic Provençal/Catalan aioli.
Source: Food Network — What Is Aioli?