Liability insurance is a very broad superset that covers legal claims against the insured. Many types of insurance include an aspect of liability coverage. For example, a homeowner's insurance policy will normally include liability coverage which protects the insured in the event of a claim brought by someone who slips and falls on the property; automobile insurance also includes an aspect of liability insurance that indemnifies against the harm that a crashing car can cause to others' lives, health, or property. The protection offered by a liability insurance policy is twofold: a legal defense in the event of a lawsuit commenced against the policyholder and indemnification (payment on behalf of the insured) with respect to a settlement or court verdict. Liability policies typically cover only the negligence of the insured, and will not apply to results of wilful or intentional acts by the insured.
Formal self-insurance is the deliberate decision to pay for otherwise insurable losses out of one's own money. This can be done on a formal basis by establishing a separate fund into which funds are deposited on a periodic basis, or by simply forgoing the purchase of available insurance and paying out-of-pocket. Self-insurance is usually used to pay for high-frequency, low-severity losses. Such losses, if covered by conventional insurance, mean having to pay a premium that includes loadings for the company's general expenses, cost of putting the policy on the books, acquisition expenses, premium taxes, and contingencies. While this is true for all insurance, for small, frequent losses the transaction costs may exceed the benefit of volatility reduction that insurance otherwise affords.
The main difference between collision and comprehensive coverage comes down to the question of what the driver controls. Collision insurance will cover events within a motorist's control or when another vehicle collides with your car. Comprehensive coverage generally falls under "acts of God or nature," or things that are typically out of your control when driving. These can include events such as a spooked deer, a heavy hailstorm, or a carjacking.