Liability
Liability coverage is offered for bodily injury (BI) or property damage (PD) for which the insured driver is deemed responsible. The amount of coverage provided (a fixed dollar amount) will vary from jurisdiction to jurisdiction. Whatever the minimum, the insured can usually increase the coverage (prior to a loss) for an additional charge.
An example of Property Damage is where an insured driver (or 1st party) drives into a telephone pole and damages the pole, liability coverage pays for the damage to the pole. In this example, the drivers insured may also become liable for other expenses related to damaging the telephone pole, such as loss of service claims (by the telephone company), depending on the jurisdiction. An example of Bodily Injury is where an insured driver causes bodily harm to a third party and the insured driver is deemed responsible for the injuries. However, in some jurisdictions, the third party would first exhaust coverage for accident benefits through their own insurer (assuming they have one) and/or would have to meet a legal definition of severe impairment to have the right to claim (or sue) under the insured driver’s (or 1st Party’s) policy.

Full Coverage
Full coverage is the name commonly referred to as Comprehensive and Collision. Insurers generally do not use this term because it implies broader coverage than actually exists.

Collision
Collision coverage provides coverage for an insured’s vehicle that is involved in an accident, subject to a deductible. This coverage is designed to provide payments to repair the damaged vehicle, or payment of the cash value of the vehicle if it is not repairable. Collision coverage is optional, however if you plan on financing a car or taking a car loan, the lender will usually insist you carry collision for the finance term or until your car is paid off. Collision Damage Waiver (CDW) or Loss Damage Waiver (LDW) is the term used by rental car companies for collision coverage.

Comprehensive
Comprehensive (a.k.a. - Other Than Collision) coverage provides coverage, subject to a deductible, for an insured’s vehicle that is damaged by incidents that are not considered Collisions. For example, fire, theft (or attempted theft), vandalism, weather, or impacts with animals are types of Comprehensive losses.

Uninsured/underinsured coverage
Underinsured coverage, also known as UM/UIM, provides coverage if an at-fault party either does not have insurance, or does not have enough insurance. In effect, your insurance company pays your medical bills, then would subrogate from the at fault party.
In the United States, the definition of an uninsured/underinsured motorist, and corresponding coverage’s, are set by state laws.

Loss of use
Loss of use coverage, also known as rental coverage, provides reimbursement for rental expenses associated with having an insured vehicle repaired due to a covered loss.