Titebond original is one of the most popular PVA glues among guitar builders. Sometimes these glues are referred to as "yellow glues". This and equivalent glues are probably the single most common wood glues in the guitar world. Used for every task in guitar making.
CA (super glue) comes in a number of varieties and is used a lot by guitar makers for fixing all sorts of things rather than for major components. Some people use it for stabilizing cracks for example. For guitar making the viscosity is very relevant. For some purposes viscous gel is more appropriates, for others a very runny glue which will penetrate the wood is more useful.
Hot animal glues. Used for everything above. The original general purpose carpenters glue. Depending on the animal source it varies a bit in regard to flexibility and open time. So for example rabbit skin glue is more flexible is used in book binding and also for sizing canvas. Fish glue is used for some purposes but I have no experience of it.
Some "boutique" guitar makers today use HHG almost exclusively. A sure way to start and argument here is to claim that either HHG or Titebond is better.
Most makers probably have both these on the shelf.
Expoxy. Some makers use these for a few purposes. I hate to smell so I avoid it. Widely used in boat building.
For plastic bindings a completely different type of glue may be used - rather like what you use for fixing bicycle tube punctures. The name escapes me. I will check a tube later if I have one.
CA and epoxy come in lots of variations so the trick with these is finding the right one to do the job. There are also good and bad versions. When you find a reliable brand stick with it.
Titebond Original became the de facto standard simply because it was reliable. Various con tries will have their own standards.
p.s. CA is great for sticking your fingers together. How do I know?