Many people consider fractures to be "partial" or "hairline" breaks of the bone.  However, fracture is the medical term that defines a break in the continuity of the bone, whether or not the bone is broken all the way through. Stress fractures, on the other hand, are hairline cracks in the bone, resulting from prolonged or repetitive force. Fractures can occur within any of the 206 bones in the human body.

There are many systems and classifications for fractures, but the four main categories are: displaced, non-displaced, open (compound–bone punctures the skin), and closed.

Further Reading:

American Academy of Orthopaedic Surgeons: Fractures