Aperture, Shutter Speed, Manual and Program (or P for Poor-fessional)
Camera Modes at Events
You noticed that Auto is not on the list. If someone had just now asked me whether my cameras have the green setting, Auto, I might have to look because I haven't thought about it in years. I am used to just feeling my way by tactile method on the knob, going second nature between Av, M and Tv. I don't even remember the direction to turn for P any more (kidding).
Wedding scenes can change every hour or faster. You can be in a church one minute and on the beach ten minutes later. You can go from needing multiple flashes to a single hi-speed flash. You can go from Manual exposures indoors to Aperture priority outdoors, to Shutter priority for controlling your maximum flash synch.
Auto actually does have a place, and that's when you go to a personal family get-together, don't mind shooting jpegs, and want your images to look like higher quality versions of point and shoot cameras.
Balancing natural light with flash at events
Many wedding photographers today are not very comfortable balancing flash with natural light. Admirably, they do not want their images looking flat-lit from an overpowering on-camera flash unit. But many have decided that they will be just natural light photographers. In part, this has been promoted by high profile speakers whose videos show them shooting wedding without any flash unit in sight, and certainly not on the camera hot shoe. Unfortunately, these instructors in some cases don't explain that natural light was a choice for that scene and not necessarily a universal solution to all of their event coverage.