There are two main ways of Riding,English and Western.
Western,has a horn on the pommel. And is very distinct...
The English saddle is more elegant and ways much less. But does not have a horn.
Halters-Halters are usaully used when not riding,To tie a horse to groom and so on.
Lead Rope- To lead the horse.It is a piece of rope that attaches to the horses halter under the neck.
Cross Ties- Connects to the halter.Used when grooming,etc.