Depending on the country/continent:
Europe - motor third-party insurance
Canada, USA - automobile/car/motor vehicle liability insurance

third party insurance -- covers just third party -- ubezpieczenie od odpowiedzialnosci prawnej;
See below:
"third party insurance
The insurance of a person's legal liability (that is, a contract between an insurer and the insured person) to cover against causing injury to another person or persons (the third party) or loss or damage to their property. An example in the UK is third party motor insurance. In the event of the insured causing damage to a third party's vehicle, his/her insurers would be liable to reimburse the third party. However the insured would not be able to claim for damages to his/her vehicle. Comprehensive insurance would be required for this."
of http://www.finance-glossary.com/terms/11438.htm

In Europe: third party, collision, and comprehensive insurance.

"Motor Insurance - Guide
Types of insurance
There are three main categories you can choose from - 'comprehensive', 'third party, fire and theft', and 'third party only'. Which you select depends on how much risk you want to take, and how much you want your insurer to take for you. Obviously, you will pay more for a comprehensive policy.

Third party only
The minimum level of cover required by law to drive in the UK. Covers you for the cost of any claims for damage you may do to another person, vehicles or property. If you are in an accident which is your fault, the insurer will pay your liability to the other people in the accident. You're not covered for damage, loss or theft of your own car or possessions.

Third party, fire and theft
Includes third party cover, and also insures your own car for damage or loss caused by fire or theft. You have to pay for damage to your own car or possessions, apart from loss caused by fire or theft.

Comprehensive
Covers you for third party fire and theft, and in addition damage to your own vehicle. There may still be some exclusions so always check. Some insurers may refuse comprehensive cover to high risk cases. Usually more expensive, but the most popular type of policy in the UK, accounting for over 70% of policies sold."
http://www.iii.co.uk/insurance/?type=motor

In USA there is Liability insurance, collision, no-fault, and comprehensive insurance.

"Automobile Liability Insurance: Protection for the insured against financial loss because of legal liability for car-related injuries to others or damage to their property. "
http://www.rhodeswilliams.com/Glossary/glossary.html

"Liability Insurance
Colorado requires all owners and operators to carry "Liability" insurance. "Liability" insurance covers the damages suffered by other people, and damages to other people's property, as the result of the owner's, or operator's, own negligence...
No-Fault Insurance
"No-Fault" insurance provides personal injury protection ("PIP") benefits to persons injured in auto accidents regardless of who was at fault for the accident..."
http://www.chalatlaw.com/autoinsurance.html.

"..."Collision" pays for repairs to your car when you're involved in an auto accident regardless of who was at fault. After a deductible is reached, your insurance company will be responsible for repairs to your car.
"Comprehensive" is for damage to your car that's not caused by an auto accident. Theft, fire, storm damage are common causes of damage that are covered. ..."
http://www.familyresource.com/finance/12/89/

I know this answer is loooong, but I wanted to provide you with sufficient explanation. Cheers, Agnieszka