Sit down means to rest in a seated position from a standing position. Sit up means to rest in a seated position from a lying position. If you walk into a room, you sit down. If you're lying in bed, you sit up. You're right, though; the end result is the same.

You can also sit up if you are slumped down in your chair, like hunched over or in a bad position.

because English's goal is to confuse foreigners. :)