Pete ailoi is not mayonaise , ugggghhhh such a naive ignorant mistake for a foodie/chef/anyone with a computer that loves food..... This is the one thing that pisses me off because I've had real aioli and I recognize the pain it is to make it.....
Aioli is a CONDIMENT not sauce, not derived from mayo. It is from Provence France it is done in a mortar and pestle, it is an emulsification of exactly what the name says(once again names do not lye) garlic, oil, sometimes lemon is added and egg yolk is added for a permanent emulsion. This is never perverted by adding anything else to it other then mustard and is only eaten with bread, nothing else.
Mayonaisse or correctly worded mahonaisse is a sauce or condiment created on an island off of Spain in a city called, get ready for this, MAHON, this is just a simple emulsification of egg yolk and oil and was created because the shortage of Milk on the island (too hilly or mountainous to raise cattle)
Tartar sauce is named after the tribe of called the tartars of the Ukraine west of the Mongolian tribes, steak tar tar is also named after them and they would eat the 2 together. They were a tribe that traveled on horseback they would put raw beef under their sattles with salt and oil, onions and wild herb in a pouch that hung off the side of the horse, as they traveled the beef was tenderized and the liquid in the pouch became emulsified. So that isnt really a "derivative" of mayo either..
But I'm not saying with today's technology all these sauces cant be made similarly to one another, so i can see where confution begins.... Hopefully I have cleared up some heads...
Oh boy... where do we start...I'm going to simply say for now that your interpretation is one based upon a fairly late 1700's plus viewpoint. There are more and much earlier viewpoints.