The general rule of thumb is that assurance is against something that will happen and insurance is against something that could happen. So in the case of life, assurance its a policy that WILL payout on death, where as with the insurance you just day it in case you die, there's no definate payout. Thats way with assurance the premiums are more.
Generally, as WoWo says, an insurance policy pays out on something that may or may not happen (such as a fire or burglary), and assurance on something that will happen, which is certainly death. But these days insurance companies are not keen on reminding people that the grim reaper is coming for them, and refer to most policies as "insurance".
A "life insured" is the person who, if they shuffle off this mortal coil, will trigger a payment of money from a policy to the...
..."life assured", the beneficiary.