I do eventing and it's a combination of showjumping, XC and dressage and your penalty points are added up and the person with the least penealities wins. The XC phase at low levels is about 2-3kms and the jumps are solid (don't fall down no matter how hard you hit them - *new releases on some jumps for te higher classes are being introduced to make the sport safer). You have an optimum time to complete the course and a 20 second window under that optimum time to be within otherwise you will get penealties for being too fast or too slow therefore you often need a very active canter or gallop. You also have jumps into water, off ledges and on hills up and down. You need a brave horse and rider but if you both train and trust each other you will be amazed at how forgivinf your horse can be when you get it wrong.
Cross country is an endurance like course. You ride so many miles with so many fences and whoever has the fastest clean round wins. Most cross country is paired with dressage and show jumping for a 3 day event.
The hunters are entirely different than show jumping, and are NOT judged on equitation. Hunt-seat eq is judged on your equitation, but not actual hunters. Hunters are judged subjectively, and in a nutshell, the horse is being judged. Showjumping is judged objectively, the fastest clean round wins. They are two ENTIRELY different sports. As for cross country, I can't speak too much because I've never competed in it, but typically it is one of the phases in a eventing. It is usually an outdoor course with permanent, "natural" jumps. From what I understand, cross country is done at a gallop, which is another difference from the hunters, which is typically at the canter. Hope that helped clarify things :)