Well I live in England and there are lots of differences again.
Boarding/Agistment = is called livery in the UK. There are 4 main types: grass (where your horse lives out 24/7) DIY (you rent a stable and field but do all the work yourself) Part (differs but your horse is generally looked after during the week then you do the work yourself on weekends) Full (your horse is totally looked after for you).
Facilities differ for all types of livery, it could be very basic, just a field and stable to having everything.
Livery yards are simply known as yards are all privately owned and are generally managed by the yard owner although some of the top yards will have an employed manager. A lot of the farms here also rent out their fields and stables (if they have any). Prices vary greatly.
Rugging: depends on the horse and owner. Some people like to rug their horses 24/7 especially if they are show horses, even if they are not you will quite often find horses wearing fly rugs throughout the summer. Most people though only rug their horses during winter and a lot never rug their horses at all. We have a high number of hairy native breeds/cob type horses that really don't need to be rugged.
Clipping: is very popular and just about every horse that is ridden throughout the winter will have some form of clip. Some people will get over zealous with their rugging though and you will find some poor horses wearing about 4 rugs when they don't need it
Trainers: (generally called instructors) are available everywhere, some of the better yards will have a resident instructor and also visiting ones although you can hire whoever you want to come and teach you in most cases. If your yard does not have an area to school in then you will be able to hire on at a local yard that does.
Discipline: If you want to know what people do with their horses, you ask just that what do you do with him/her. Hacking is the most popular pastime. Western riding is not so common as in America but it is becoming quite popular. Show jumping, dressage, eventing and showing are the main competitions here and there are shows on every week of the year. Unlike Australia we win rosettes and unlike America Red is first place!
Riding is a very popular sport here but we are a small country and a lot of our countryside/bridlepaths have been taken over so for a lot of us riders we ride in built up areas, negotiating heavy traffic, childrens playgrounds etc.