There are many reasons why riding the PCT is different from hiking it. The biggest one is logistics. (Riders have ten times the pre-trip planning required of hikers.) But there are additional differences every step of the way.
The whole first 200 miles of the trail must be assumed to be completely without food or water for you or your horse. It is not possible (or practical) to carry all food and water with you, however, given the amount your horses will eat and drink. Thus, riders typically arrange for helpers to "cash" supplies of hay and water for them along the trail, or they cash these stores themselves, getting off the trail every few days to drive ahead and leave what they will need for the next stretch. This requires someone's help moving your trailer from where you start off to where you will need it next, or it requires two trailers and a lot of hitchhiking. In theory, this could be done alone but the vast majority of riders have a support team arranged to help them with these kinds of logistics.
Typical horse shoes wont last more than 3 weeks at a time on the PCT. Boots require regular trimming and your horses will, just in general, require more care than usual of all kinds. Resources for these things (farriers, vets, chiropractors, etc) are going to be needed the entire length of the trail.
Hikers periodically detour to a select town to pick up pre-arranged packages mailed to them to re-stock their food and gear. At these times they often have the opportunity to sleep a night in a real bed, get a shower and rest from the riggers of the trail. This ability to take a semi-break once in a while can be the difference between finishing the trail and giving up mid-way through.
Riders need this kind of rest to, as well as a chance to pick up re-supplies at prearranged mail drops. But for them it's not so simple. Some towns wont allow you to ride a horse in the town limits. In order to spend the night in a "real bed" you have to have somewhere to board your horse. And you can't just mail yourself a bail of hay. A lot more planning has to go into your stops than those of a hiker.