A Brief Thesis on Hamburger Related Sauces:
In-n-Out calls it "Spread". Mc D's calls it "Special Sauce". The uninitiated may just call it "a mixture of mayo, ketchup and mayo". The masses can't seem to come to agreement on a universal term, and I contend that it would be best if we had one.
"Spread" and "Special Sauce" are weirdly vague and, well, trademarked. I've heard some use "Burger Sauce", and this is the term I use. Versions of "Burger Sauce" have become so commonplace over the past couple decades that it is no longer just a unique invention of particular institutions anymore, it's part of hamburger culture in general.
This type of sauce is unique to burgers. "Burger Sauce" just makes sense. It's a term that's in the public domain, descriptive, but not restricting. You know what you're getting: a mayonnaise based sauce for your hamburger.
I sometimes think too much about hamburger stuff.