Human skeleton
There are over 206 bones in the typical adult human skeleton, a number which varies between individuals and with age. Human babies are born with 270 soft bones that fuse together by the age of twenty or twenty-five into the 206 hard, permanent adult bones.
Human Appendicular skeleton diagram (from Wikimedia)
Human Axial skeleton diagram (from Wikimedia)
The axial skeleton has 80 bones together and includes the skull, the spine, the ribs and the sternum (breastbone).
The appendicular skeleton has 126 bones. This includes the two limb girdles of the shoulders and the pelvis) and their attached limb bones (arms and hands, legs and feet).
Horse skeleton diagram (from Wikimedia)
Horse skeleton
Horses typically have 205 bones.
The axial skeleton contains the skull, vertebral column, sternum, and ribs. The appendicular skeleton contains the fore and hind limbs. Unlike his human rider the horse has no collarbone, plus the horse is able to lock the legs to rest and sleep standing up.