Hard reset often means resetting the whole thing; to a blank slate while a soft reset may be something like a rebirth where it makes getting to a certain point easier or lets you upgrade certain things permanantly.
both reset both in different ways; A hard reset (as mentioned before) essentially deletes all saved data, while a soft reset will maintain the previous data to make the game easier to progress, so in a sense it remeves the ammount of kills and stats in exchange for this or that to help the player progress faster, while maintining the "lifetime" ammount of each data set.