Let's use the aftermath of Superstorm Sandy as an example to illustrate the differences between collision and comprehensive. Within that storm, let's consider two events that might have happened: 1) a heavy tree branch fell on your car, or 2) you swerved to avoid a falling tree branch and wound up crashing into a tree. In the first event, you had no control over when or why a tree branch would fall on your car. This kind of accident would get reimbursed under your comprehensive policy. In the second situation, you were driving the car and ultimately swerved into the tree, which makes it a collision, and collision insurance therefore pays for the damages. Events like the hypothetical ones stated above are why it's important to differentiate between the two types of coverage.

In most countries, third-party or liability insurance is compulsory insurance for any party that may potentially be sued by a third party. Public liability insurance involves industries or businesses that take part in processes or other activities that may affect third parties, such as subcontractors, architects, and engineers. Here, the third-party can be visitors, guests, or users of a facility. Most companies include public liability insurance in their insurance portfolio to protect against damage to property or personal injury.
Bodily injury coverage is written with two limits: the first applies to each person; the second is related to each accident. As an example, minimum recommended coverage levels are usually $100,000/$300,000, which translates to policy limits of $100,000 per person in an accident and $300,000 total per incident. Required coverage levels vary by state, but can be as low as $10,000/$20,000, which is hardly sufficient for a serious accident.
If you have paid off your car, comprehensive coverage is optional. It may be a good idea to find out the Kelley Blue Book value of your vehicle. Would you be able to pay that amount to repair or replace your vehicle if it were stolen or damaged in an accident? If you can't afford to pay much out of pocket, then buying optional coverages, like comprehensive coverage and collision coverage, may be a smart investment.