Slight correction: the abbreviation for Artificial Super Intelligence is ASI, it's the more capable version of Artificial General Intelligence (AGI) which itself alredy is miles ahead of mere Artificial Intelligenge (AI) which is sometimes also refered to as "narrow AI"
The difference is that AI can posses superhuman capabilities on a specific field but not on every field. AGI is the same except you don't need a different software for different tasks because due to being generally intelligent it can do it all. ASI is what you get when AGI starts improving itself and then this improved version creates even better version of itself and so on leading to singularity or "intelligence explosion" resulting in superintelligent being which would effectively be a god.