Any headgear meant to protect from cranial injury may be called a protective helmet. Helmets designed to protect from bullets and shrapnel are called ballistic helmets.
Modern safety helmets work so to deflect and dissipate any impact coming toward the wearer. They are designed to push the force to the opposite part of the helmet.
Many. Aside from ballistic helmets, there are bump helmets, driving helmets, construction helmets and many others, depending on which type of injury is most frequent in that job.