These two terms are somewhat interchangeable. However, the term hoof usually refers to the horny external part of that makes up the hoof wall plus the sole and the frog. When we are talking about a horses foot we are speaking about the internal parts that encompass the bones, tendons, ligaments and blood vessels.
There is an old saying. "no foot no horse" . This is something that new horse owners need to think about. Without healthy feet the activities that you intend to participate in will be very limited. A healthy foot comes from genetics and environment. So knowing something about a horses parents will give you some idea of what to expect from their offspring. Environment can be controlled by the owner of the horse. This would include nutrition, exercise, sanitation and moisture.
Horse owners should know the parts of a horse foot to be able to discuss problems with the farrier or veterinarian.
The parts of the hoof that you can see are the hoof wall, the frog and the sole. These parts are much like your finger nails in that they are insensitive because they do not contain blood vessels or nerves. They can be trimmed, rasped and nailed without causing any pain.
The White line is the junction between the insensitive outside and the sensitive interior of the foot.
The bars are the V shaped part of the sole and are portions of the hoof wall.
The sole is the hard material that is the bottom of the hoof. It should be concave in shape so that it does not touch the ground.
The frog lays between the V and is rather rubbery. It will provide some traction and will protect the interior sensitive structure and allows expansion and contraction as the horse puts weight on the foot. Collateral clefts or sulci separate the frog from the bars and sole. The deep groove in the center of the sole is called the center cleft. It is the center of the frog.
The heel bulbs are the rounded area at the back of the hoof . This is where the frog joins with the skin of the foot.
The coronary band or coronet is a ridge around the top of the hoof. It is soft and produces hoof growth. Sort of like your fingernails grow from your cuticles.