The surgeon should decide what procedure is the right one for you, as an individual. Some people insist on a particular one because they're been reading about the latest fad, but that's silly. My surgeon said I needed a "Toupet" because of "wimpy" swallow. It's not the same as a floppy Nissen, just not totally wrapping all the way around the esophagus.
There was a question going in about whether I'd need another procedure to make the esophagus longer, but they were able to "free up" enough (cut loose up in the chest) to get the wrap down below the diaphragm.
They'll only tell you what they think you need to know. Most people are blithely ignorant of anatomy and wouldn't understand anything beyond pulling down the stomach. If you're lucky, surgeon might give you a brief explanation if you ask. But you might still get something else in OR when they actually see what they're dealing with.
No use worrying.