Your buying decision should not be solely based on price alone, there are significant differences in coverage provided and the carriers available. Policies should be fully understood before purchasing. In a case of an accident, having the right amount of insurance can benefit you personally, financially, and legally.
Whats the Liability Insurance VS Collision Coverage (full coverage)?
 There are two main components to Auto Liability: Bodily Injury and Property Damage liability.

• Bodily Injury Liability helps pay for the costs associated with another person’s injuries, including medical expenses, loss of income and pain and suffering.
• Property Damage Liability takes care of any expenses that arise from damage caused by you to another driver’s vehicle or property.

• Property coverage pays for damage to or theft of your car.
• Liability coverage pays for your legal responsibility to others for bodily injury or property damage.
• Medical coverage pays for the cost of treating injuries, rehabilitation and sometimes lost wages and funeral expenses.

An auto insurance policy is comprised of six different kinds of coverage. Most states require you to buy some, but not all, of these coverages. If you're financing a car, your lender may also have requirements.

Most auto policies are for six months or a year. Your insurance company should notify you by mail when it's time to renew the policy and to pay your premium.

Why do you need auto insurance?
It's really all about protecting yourself financially.

• If you're in an accident or your car is stolen, it costs money, often a lot of money, to fix or replace it.
• If you or any passengers are injured in an accident, medical costs can be extremely expensive.
• If you or your car is responsible for damage or injury to others, you may be sued for much more than you're worth.
• Not only is having insurance a prudent financial decision, many states require you to have at least some coverage.

Questions to ask your agent
Your Independent Agent is an advocate for finding auto insurance that meets your specific needs. Here are a few things to consider as you prepare for the discussion:

• How much can you afford to pay if you get in an accident? (To keep premiums low you may want to have a higher deductible and be willing to pay more for repairs.)
• What is the insurance company's level of service and ability to pay claims?
• What discounts are available? (Ask about good driver, multiple policy and student discounts.)
• What's the procedure for filing and settling a claim? (Ask who to call and what happens after you file a claim.)

Liability

Investopedia explains 'Liability Insurance' Liability insurance is very important for those who may be held legally liable for the injuries of others, especially medical practitioners and business owners. A product manufacturer may purchase product liability insurance to cover them if a product is faulty and causes damage to the purchasers or any other third party. Business owners may purchase liability insurance that covers them if an employee is injured during business operations.

  Umbrellapolicies: A policy designed to provide protection against catastrophic losses. The umbrella policy serves two main purposes: it provides excess limits when the limits of the underlying liability policies are exhausted and it provides protection against some claims not covered by the underlying policy, subject to the assumption, by the named insured, of a self-insured retention

"One day while driving home from work, Ms. Smith  crashed into the rear of a car on a slick highway. A woman and a child were critically injured and the child was paralyzed . After two years of litigation, Ms. Smith settled the lawsuit for more than $2 million. The client had $5 million in umbrella coverage. The policy paid for the settlement and all legal costs. “Without the umbrella,” Ms. Smith said, “they would have been completely wiped out.” " And now think of this scenario as if she didnt have umbrella, many individuals do not.  So what would have happened then? The insurance company would have paid the liability that Ms. Smith carries on her policy to the injured party, which 60% of policy holders carry less than $100,000, and the remainder of that would have been billed to Ms. Smith! The court would hold Ms. Smith liable to pay the amount of $1,900,000.
It is so important to be properly protected because you never know what could happen! 

Personal Umbrella insurance is additional liability insurance, designed to pay out on top of your existing auto and homeowner’s/renter’s insurance policies. For example, you may only have $300,000 in liability coverage on your car insurance. If you are hit with a claim of $1,000,000, you would be on the hook for $700,000 yourself unless you had an adequate umbrella insurance policy. Here is a diagram explaining this from MSN Money: