These two closely related words are not the same and are not synonyms.
To ensure is to take action in order to make sure that something is true, will happen or, indeed, is sure. Close synonyms are ‘to make sure’ and ‘to check‘.
Examples:
It is important to ensure that your car doors are locked before leaving the vehicle.
Ensure that you disconnect the appliance from the power source before undertaking any maintenance work.
NB: In simple English, “Unplug the device before servicing.”

To assure is to make oneself, or someone else, feel feel more confident or sure about something.
Examples:
Seeing his sideways look assured me that the man really was hiding something.
The child was really nervous about the school test, but his teacher assured him that there was nothing to worry about.
Life Assurance (a private pension scheme) gives one a feeling of assurance about financial security after retirement.
Self-Assured means confident (normally positive).