These terms are now typically used interchangeably, meaning the same thing. However, they have been used to describe two different types of life cover plan.
Assurance is something which is 'assured' (or guaranteed) to happen, in this case when you pass away. A life assurance plan therefore pays out 'when' you die, rather than 'if' you die.
Insurance is based on something which might happen (again you passing away), during a specific time period (or term). Life insurance is for a fixed time period, and will pay out should you pass away within that time frame. If you haven't passed away within that time frame, the policy comes to an end and you are no longer covered.