Those are just fries. Definitely NOT wedges.
I was introduced to fry sauce last July, on a trip to central Washington. The waitress asked if I wanted some with my fries, and when my face went blank the locals I was with said “YES!” They were so, so right. 
And it actually varies by location too! The fry sauce I get here in Oregon tastes different depending on which ‘fast food’ restaurant I go to. We have a local place here called Nancy Joe’s that makes the best, imo.
Okay, I’ll ask the obvious question: What the hell is “fry sauce”? :dubious: 
It’s a mix of…something…? I dunno. Maybe mayo and ketchup? And some spices…I just know it’s usually orange and delicious.
I agree with AngelSoft. Typically a mix of ketchup and mayo, but it can be sexed up with some powdered spices and/or Worcestershire and the like, as well. But ketchup and mayo are the base.
Around the only thing I can stand that has mayo in it is the fry sauce-ish take at a certain Columbian-Cuban restaurant, which is loaded with so much garlic that it overpowers the insipidness of the mayo.
Similarly, I’m not a fan of mayo on burgers, but I will accept it in “hamburger sauce” (which typically starts with a combo of mayo, ketchup, and relish.)
Sounds like 1000 Islands salad dressing to me. :o
Yes, many versions of hamburger sauce can be thought of as a variation of Thousand Island. And fry sauce can be thought of similarly as a “Russian dressing” variant. (Though I’m sure there are versions of both that stray from the most common variations I’ve seen.)
Fry Sauce is basically 1000 Island without the pickle relish. It’s a Utah thing (along with Southern Idaho).
Throw some coleslaw on the burger and then put that Thousand Island type sauce on top and you have one of my favorite burger variations.
Intereting. I had no idea. I’ve definitely seen it around here, too. Freddy’s Frozen Custard and Steakburgers, with locations throughout the Midwest and beyond (based out of Wichita, KS) has it, for example. It does look like it’s most associated with Salt Lake City, but it is seen beyond there.
Indeed, the fries in the Eamonn’s picture are a very common configuration for fries in the U.S. McDonald’s-style super-thin fries are not the most common style.
I will have you know that despite this thread I had mashed potato at lunch. 
Bangers and mash with mushy peas? :o
My local grocery store has their own store brand of fry sauce. I attribute that to the enormous number of Mormons in these parts, jonesing for a taste of Salt Lake. 
They don’t have animal-style fries.
That’s because it’s a French Fry chart, not a “Things You Have To Do To Make In-N-Out Fries Edible” chart. 
It looks like its design may have been influenced by Archimedes’ Screw, or vice versa.