In alpine skiing in North America, most resorts have their own ski school staff, whereas in Europe, you are more likely to find a ski instructor servicing a particular hotel. Instructors are trained and certified by their national organizations (i.e. in Canada the Canadian Ski Instructors Alliance), which may certify their instructors in an 'international' level, which is overseen by the International Ski Instructors Alliance.
Most ski schools teach a variety of skills to a variety of people who are at grossly differing skill levels. For example, their might be programs for: toddlers, children, teens, or adults beginner learning the basics, race programs for all ages with vastly different competition levels, freestyle or mogul teaching, and finally, my favourite: terrain park/half pipe programs. Of course, ski schools also spend a great deal of time training their own staff.