In order to make mayo, an emulsion, you need oil, acid (vinegar or lemon juice) and egg yolk.
How can you make mayo without oil and egg yolks? How can manufacturers get away with calling whatever mayo-like substance in those jars “mayonnaise”. Have I spelled mayonaisse right at least once in this post?
Short answer: Who cares and why would you even want to know?
Long answer: Who cares and why… oh, er, well they probably replace the egg yolks with some industrial detergent that has a similar flavor and make up for the lack of texture by adding granulated Naugahide.
I would sooner die of congestive heart failure (and probably will) before I will ever willingly eat such tripe. In fact, even tripe sounds far more appealing than such unmitigated dreck.
Short answer: yup, you spelled it “mayonnaise” in the OP subject and the first time in the OP itself.
Long answer (without so much bile ;)): The jar in my fridge says “Fat Free Mayonnaise Dressing.” Since the M-word itself is an adjective used to describe a type of dressing (named, apparently, after the French conquest of the Spanish city of Mahon [accent on the “o”] in 1756), it can probably be liberally used to describe any number of things without legal ramifications. Except, in the US, law states that full-fat mayo must contain at least 65% oil by weight.
In the low-fat/non-fat variety, they replace this with stuff like food starch and water. Interestingly, it still contains vinegar and egg, just in lower proportion.
Oh, and Zenny? There are those of us who don’t see that much difference between one sandwich/salad lubricant and another, used as such. Sure, if I were to sit down to a blind taste test of the pure products, I could probably easily tell them apart. I’d also have to go clean my tongue with baking soda on a wire brush afterwards. For my money, I’d rather save that amount of artery clog for a good steak. 
Bon appétit!
Try visiting one of my first threads at these boards; the “Mayonnaise Combat Thread”, for more insight to the nausea inducing substance known as Miracle Whip and its Satanic brethern.
http://boards.straightdope.com/sdmb/showthread.php?threadid=35389
Hee hee. I have a dirty mind.