'Security' and 'safety' are two different concepts, although inevitably there is some degree of overlap. 'Security' is about avoidance of crime, while 'safety' is about avoidance of danger. So, for example, in a car, seatbelts and airbags are safety features, whereas the anti-theft alarm is a security feature. If you feel 'safe', it suggests that you feel you are out of danger. If you feel 'secure', it it's more to do with feeling psychologically comfortable - the opposite of insecure.