Emulsions can be permanent, like mayo, or temporary, like an oil and vinegar salad dressing that will separate. Aioli and mayo are both permanent emulsions because they have stabilizing ingredients.
And mayonnaise? If it's not a salad dressing, it's definitely salad dressing's creamier sibling. Beyond just slathering your favorite salad dressing on a bun, though, get a little creative.