A car crash on Jagtvej in Copenhagen, Denmark.

A car crash on Jagtvej in Copenhagen, Denmark. (Photo credit: Wikipedia)

Insurance and assurance are different concepts. Insurance is the better known and most of us have bought an insurance policy for our car, for example.
A ‘third party’ insurance policy covers us for damage that we might cause to other persons, vehicles or property. Third-party insurance is usually the minimum policy as regards vehicles.
A ‘third-party, fire and theft’ policy also covers us if our vehicle catches fire, or if it is broken into or stolen.
Fully comprehensive insurance covers pretty much everything, including the results of one’s own bad driving. Naturally, such cover is the most expensive.
Each year of claim-free driving earns us a percentage bonus, reducing the cost of insurance in the future. Making a claim on the insurance may remove that bonus.

Assurance can be a kind of life insurance, aimed at assuring the survivor’s future in the event of the insured’s death.
Assurance is also a  close synonym of :
1. A declaration or promise
2. Certainty
3. Self confidence