Well, each discipline has its own framework and categories.
In general, shows and classes can be categorized several ways.
My examples are going to be from English competition but the same principles applies to Western, I’m sure.
Shows can be categorized by the size of the competition area, that is local, state or provincial, regional, national. Often there is a progression where people qualify locally or regionally to participate in the national level shows.
Classes in shows can be categorized by the level of difficulty of the task. For instance, you can have jump classes where the fences are two feet, two feet six inches, two feet nine inches, three feet, one metre, etc. Or you can do dressage level one, level two, level three, Grand Prix, etc. I think that in sports like reining, you also have different levels of difficulty.
Classes can also be further differentiated by the age or experience of the horse and/or the rider. You can have classes for two year old horses, classes for junior riders, classes for horses that have not yet won a ribbon in the discipline or are in their first year of showing. There are clear rules in each discipline about what separates an amateur from a professional. In general, a professional is earning money giving riding lessons or training horses, and an amateur is not.
A show can be either local or national and have all these separate classes. Obviously the competition will be stiffer at a national level especially if everyone has to qualify locally to get to the national show.
Anyhow, you need to find the governing body that oversees the discipline that you are competing in (pleasure? reining? halter? A particular breed organization?) and download their rule book. Everything will be in there, in great detail.