I think you're in Japan ? Car manufacturers fit different system to cars depending on the market they are being sold in. So what you have on your Japanese-spec Jazz reflects local regulations and expectations. UK-spec cars do not necessarily mirror that, but it is interesting to hear what the Japanese market requires. At least Japanese cars have the steering wheel on the correct side of the car !
So we don't get adaptive cruise control, and we have something called Lane Departure Warning, which just alerts the driver should the car perceive you are veering out of a marked lane. Your Lane Keeping Assist and Road Departure Mitigation sound similar but from your description may actively steer the car. Personally I find the idea of needing systems to prevent you driving off the road, or to avoid a pedestrian, pretty worrying: others have commented previously about such systems encouraging the driver to "switch off" rather than concentrate on what he/she is doing.