Plasty is a term that means plastic or restorative surgery. Both operations are used to repair fractures in the main body of the vertebra. Kyphoplasty is actually a type of vertebroplasty.
Vertebroplasty is the injection of bone cement into the fractured vertebral body. A long, thin needle is inserted through the skin into the bone. The cement is injected through the needle into the bone.
With kyphoplasty a deflated balloon is put through the needle into the fractured bone. The balloon is inflated to restore the size and shape of the collapsed bone. Then the bone filler cement is injected. With the kyphoplasty, the some of the height of the bone is restored.
Both methods are very technical. High quality imaging equipment is needed to perform these operations. The advantage of the kyphoplasty is improved spinal alignment. There's also less chance the cement will leak into the body causing other problems.